If Then Statements in Logical Reasoning

📑 On this page

⚡ The 20-second answer

Turn every rule into an arrow: “if A, then B” and “A only if B” are both A → B. Valid: A, so B; not B, so not A. Fallacies: B, so A; not A, so not B. “Unless” means “if not”. “Either A or B” means not A → B.

🎬 The 30-second story

The 75% rule

“You can sit end-sems only if attendance is 75% and fees are cleared. I've got 78%. I'm in!”

📋

Aarav

Aarav, on the attendance portal.

“78% gets you to the door, not through it. Fees cleared?”

🧾

Zoya

Zoya, holding his fee slip.

“Kunal had 60% and still sat the exam. So the rule is fake.”

📱

Rohan

Rohan, forwarding a screenshot.

“Either the rule was broken, or Kunal got the medical exemption in the last line.”

⚖️

Meher

Meher reads the last line.

Tara's verdict: “Only if 75%” means: sat the exam → had 75%. Not 75% → sits; that's Aarav treating a necessary condition as sufficient. Kunal sitting with 60% breaks the rule as written, so it was broken or an exception applied. The rule isn't fake, just not the whole story.

How does CLAT word conditional statements?

CLAT rarely writes “if… then”. It hides the arrow inside only if, unless, has to and either–or. Translate first, then think.

The sentence	Arrow	Seen in
If A, then B · B if A	A → B	Everywhere
A only if B · Only if B, A	A → B	CLAT 2019 Q34
B will not happen if A	A → not B	CLAT 2019 Q35
To be A, a person has to B	A → B	CLAT 2018 Q98
Not A unless B	A → B	CLAT 2022 Q112
Either A or B	not A → B	CLAT 2019 Q36

→ scroll to see more

📌 The necessary part goes at the arrow's tip

Whatever follows only if, has to or requires is necessary. It sits at the tip: A → B.

What does “if A, then B” actually promise?

Exactly one thing: whenever A happens, B happens. A is sufficient for B; B is necessary for A. It is silent about life without A. As sets, “if you sat the exam, you had 75%” is “all exam takers are 75-percenters”.

⭕ Venn check

The 75% notice, drawn as sets

Statements

▸All Exam takers are 75-percenters
▸All Exam takers are Fee payers

Conclusions

All 75-percenters are Exam takers
🤔 Possible, not certain — Aarav's leap: a 75-percenter with unpaid fees stays out.
Some 75-percenters are Fee payers
✅ Definitely follows — Every exam taker is in both circles.
Some Fee payers are not 75-percenters
🤔 Possible, not certain — Fees say nothing about attendance.

shaded = empty× = at least one lives here

Which moves are valid and which are fallacies?

⚔️ Side by side

Two safe moves, two traps

✅Valid

Forced

•A is true, so B is true
•B is false, so A is false (the contrapositive)

❌Fallacy

Feels right, isn't

•B is true, so A is true (affirming the consequent)
•A is false, so B is false (denying the antecedent)

Test	Valid	Fallacy
Rule: sat → 75%	Sat, so 75% · Below 75%, didn't sit	75%, so sat · Didn't sit, so below 75%

The contrapositive flips and negates both parts.

How do you solve any conditional question in four moves?

1
Translate to an arrow
Use the table. The necessary part goes at the tip.
2
Write the contrapositive
Flip and negate both: not B → not A.
3
Match the options
Keep the rule, its contrapositive, or a chain of them.
4
Bin the two fallacies
The reverse (B → A) and the inverse (not A → not B) are out.

How do you translate only if, unless and either–or?

Only if: the arrow points away from it

“A only if B” means A → B. A bare if introduces the sufficient part; only if introduces the necessary part. “You can vote only if you're 18” doesn't mean every 18-year-old votes.

Unless: read it as “if not”

“A unless B” means if not B, then A. “You'll miss the bus unless you leave now”: not leaving → missing it. Leaving now doesn't promise you'll catch it.

Either–or: is “both” allowed?

“Either A or B” guarantees at least one: not A → B, and not B → A. A → not B holds only if both can't happen. “Either X or Y will take the only computer” rules out both, so it adds X → not Y and Y → not X.

⚠️ The reverse sounds so right

CLAT 2019 mixed the contrapositive with the reverse and the inverse. The reverse reads naturally, which is the trap: “only if 75%” doesn't mean “75% gets you in”.

Worked examples: what follows from the rule?

✍️ Worked example Warm-up ⏱ 30 sec

Kabir's student discount

Kabir's rule: “If a customer shows a student ID, they get 10% off.” Ria showed her ID. Dev got 10% off. Sam didn't show an ID. Neha didn't get 10% off. About whom can you be certain of the other fact?

1
Arrow: ID → discount. Contrapositive: no discount → no ID.
2
Ria: ID, so discount. Certain. Neha: no discount, so no ID. Certain.
3
Dev: discount, so ID? Affirming the consequent; maybe a festival offer. Unknown.
4
Sam: no ID, so no discount? Denying the antecedent. Unknown.

Answer: Ria and Neha only

⚡ The exam-hall shortcut

Certainty comes from the if-part being true or the then-part being false. The other two give you nothing.

✍️ Worked example CLAT level ⏱ 60 sec

The fest permission chain

The college fest will be held on the main lawn only if the police grant permission by Friday. The police will not grant permission unless the organisers submit a crowd-safety plan. The organisers will submit the plan only if the fire audit of the stage is cleared. The fest was held on the main lawn. Which must be true?
(A) The fire audit of the stage was cleared.
(B) Because the fire audit was cleared, the police had to grant permission.
(C) The police granted permission before Thursday.
(D) Had the police refused, the fest would still have been on the lawn.

1
Translate: lawn → permission. “Not grant unless plan”: permission → plan. Plan → audit.
2
Chain: lawn → permission → plan → audit. The fest was on the lawn, so the end follows: A.
3
B runs the chain backwards: affirming the consequent.
4
D: no permission → no lawn, by contrapositive, so D contradicts. C: “by Friday” isn't “before Thursday”.

Answer: A

⚡ The exam-hall shortcut

Line the arrows up nose to tail. A true start gives a true end; a false end gives a false start.

✍️ Worked example Tricky ⏱ 45 sec

Maggi or sandwiches?

Main statement: “Either the night canteen serves Maggi tonight or it serves sandwiches.” Choose the ordered pair where the first implies the second.
1. It serves Maggi. 2. It does not serve Maggi. 3. It serves sandwiches. 4. It does not serve sandwiches.
(A) 1, 4 (B) 2, 3 (C) 3, 2 (D) 4, 2

1
Inclusive either–or: not Maggi → sandwiches; not sandwiches → Maggi.
2
Only B (2, 3) fits.
3
A and C assume the canteen can't serve both. Nothing says so, unlike 2019's “the only computer”.
4
D: no sandwiches should give Maggi, not “no Maggi”. Contradiction.

Answer: B

⚡ The exam-hall shortcut

Either–or gives “not one → the other”. Add “one → not the other” only when the sentence rules out both.

How has CLAT asked conditionals?

📝 Asked in CLAT 2018 · Q98 Necessary condition

The doctor is a person who looks after the sick people and prescribes medicines so that the patient recovers fast. In order to become a doctor, a person has to study medicine. Doctors lead a hard life… They get up early in the morning and go to the hospital… They always remain polite so that patients feel comfortable with them… i. Kumar Sharma wakes up early in the morning everyday and treats everyone with patience. He usually gives emergency aid to the persons who are injured in accidents. ii. Rakesh studied medicine in Russia and practiced medicine there for 2 years. Later, stopped medical practice and turned into some business. iii. Shalini works in Apollo Hospitals. She always remains polite so that patients feel comfortable. She is a specialist in providing quality care for the cancer patients.

Based on the above paragraph, who among the following is/are doctor(s)?

AAll are doctors

BRakesh and Shalini are the doctors

CKumar Sharma and Rakesh are doctors

DOnly Rakesh is a doctor

Reveal answer + reasoning

Answer: D

One sentence is a rule: to become a doctor, a person has to study medicine, so doctor → studied medicine. The rest describes doctors; it isn't a test for being one. Calling Shalini a doctor because she is polite and works in a hospital is affirming the consequent. Neither she nor Kumar is shown to have studied medicine. Rakesh studied and practised medicine, so only he meets the condition. Answer D (official key). Caveat: studying medicine alone only makes him eligible; his practice seals it. Time: 45 seconds.

Why the others fail

A — Kumar and Shalini never meet the one necessary condition.
B — Politeness and a hospital job describe doctors; they don't prove one.
C — Early mornings and first aid could describe a paramedic.

📝 Asked in CLAT 2019 · Q34 Only if

Directions: choose the ordered pair of statements where the first statement implies the second, and the two statements are logically consistent with the main statement.

Main statement: Only if the teaching standard is destroyed, will examination result be poor. 1. Examination result is poor. 2. Teaching standard is not destroyed. 3. Examination result is not poor. 4. Teaching standard is destroyed. The ordered pair of statements is:

A2, 3

B2, 4

C1, 3

D1, 2

Reveal answer + reasoning

Answer: A

Translate: “only if destroyed, will the result be poor” = poor → destroyed. Contrapositive: not destroyed → not poor. That is 2, then 3. (The rule itself, 1 then 4, isn't offered.) Our solution: A; 2019 has no official key. Time: 30 seconds.

Why the others fail

B — “Not destroyed” can't imply “destroyed”.
C — “Poor” can't imply “not poor”.
D — Poor → not destroyed contradicts the rule.

📝 Asked in CLAT 2019 · Q35 “…will not … if”

Same directions as Q34: the first statement must imply the second.

Main statement: The computer will not work if operating system fails. 1. Operating system fails. 2. Operating system does not fail. 3. The computer does not work. 4. The computer works. The ordered pair of statements is:

A2, 1

B2, 3

C1, 4

D4, 2

Reveal answer + reasoning

Answer: D

The if clause comes second, so don't read left to right. Translate: OS fails → computer doesn't work. Contrapositive: computer works → OS didn't fail. That is statement 4, then 2. Our solution: D. Time: 30 seconds.

🔬 Option autopsy

Option autopsy: CLAT 2019 Q35

Rule: OS fails → computer doesn't work. Which pair is valid?

A 2, 1: OS doesn't fail → OS fails Tag it

🔄 Opposite direction

A statement implying its own negation.

B 2, 3: OS doesn't fail → computer doesn't work Tag it

❓ Not supported by the text

Denying the antecedent: the rule is silent when the OS works.

C 1, 4: OS fails → computer works Tag it

🔄 Opposite direction

Contradicts the rule head-on.

D 4, 2: computer works → OS doesn't fail Tag it

✅ Correct

The contrapositive.

🔄 Opposite direction❓ Not supported by the text✅ Correct

Guess the trap behind each option, then tap to check. Wrong options fail in a handful of predictable ways.

📝 Asked in CLAT 2019 · Q36 Either–or

Same directions as Q34: the first statement must imply the second.

Main statement: Either X or Y will take the only computer in the room. 1. X took the computer. 2. Y did not take the computer. 3. X did not take the computer. 4. Y took the computer. The ordered pair of statements is:

A3, 1

B1, 3

C4, 3

D1, 2

Reveal answer + reasoning

Answer: C

One computer, so exactly one of them takes it: not X → Y, not Y → X, X → not Y, Y → not X. C (4, 3) is Y took it → X didn't. Valid. Our solution: C. Honest flag: D (1, 2), X took it → Y didn't, is valid by the same logic, so the question has two defensible answers. With no official key for 2019 we keep C, but D is not your mistake. Time: 40 seconds.

Why the others fail

A — “X didn't take it” implying “X took it”: self-contradiction.
B — The same clash, reversed.
D — Also valid: one computer means X taking it rules Y out. The question's flaw.

Can you spot the fallacy?

💥 Myth vs fact

Myth vs fact: conditionals

🙅 Myth

“Only if” means the same as “if”.

Tap to bust it →

✅ Fact

Opposite ways: “A if B” is B → A; “A only if B” is A → B.

🙅 Myth

“If A then B” also means “if not A, then not B”.

Tap to bust it →

✅ Fact

Denying the antecedent. B can still happen another way.

🙅 Myth

“A unless B” means B rules A out.

Tap to bust it →

✅ Fact

It only promises: if not B, then A.

🙅 Myth

“Either–or” always means exactly one.

Tap to bust it →

✅ Fact

Only when both are impossible. Otherwise it's at least one.

🎯 Quick quiz

Five arrow checks

0 / 5

The college library has a new policy. A student may borrow a reference book overnight only if they have no overdue books. Every student who borrows a reference book overnight must also leave their ID card at the front desk. On Tuesday, Meher left her ID card at the desk, Zoya had no overdue books, and Aarav borrowed a reference book overnight.

Q1. Which must be true?

Q2. “Unless the umpires inspect the pitch by 9 a.m., the match will be delayed.” The match was not delayed. What follows?

A trust's scholarship rules say that every applicant it considers has either scored above 90% in Class 12 or cleared the trust's own entrance test. No applicant who skipped the trust's interview is considered at all. This year Rohan, who scored 86% in Class 12, was considered. Tara scored 94% in Class 12 but did not turn up for the interview.

Q3. Which must be true?

Q4. What is the contrapositive of “If the server is down, the portal won't load”?

Q5. “You can join the moot team only if you clear the internal round.” Kabir cleared the internal round. What follows?

🎯 Conditionals in a nutshell

“If A, then B”, “A only if B” and “not A unless B” are all A → B.
Valid: A, so B. Not B, so not A.
Fallacies: B, so A. Not A, so not B.
“Either A or B”: not A → B; A → not B only if both are impossible.

📎 Cheat sheet

“If A, then B” / “B if A” → A → B; contrapositive not B → not A
“A only if B” / “has to” / “requires” → necessary condition → A → B
“A unless B” → “if not B, then A”
“Either A or B” → not A → B, not B → A; can both happen?
“Ordered pair … first implies the second” → find the rule or its contrapositive
“Who among them is…?” → apply the necessary condition; traits don't qualify

Frequently asked questions

What is the difference between “if” and “only if” in logical reasoning?

“A if B” means B → A: B is enough for A. “A only if B” means A → B: B is needed for A. They point in opposite directions, so “you can vote only if you're 18” means every voter is at least 18, not that every 18-year-old votes.

What are the valid forms of a conditional statement?

Given “if A, then B”, two conclusions are valid: if A is true, B is true; and if B is false, A is false. The second is the contrapositive. Concluding A from B, or not B from not A, is a fallacy, because B might have another cause.

How do I translate “unless” in CLAT questions?

Replace “unless” with “if not”. “A unless B” becomes “if not B, then A”. “You'll fail unless you revise” means not revising leads to failing. It doesn't promise that revising guarantees a pass; the sentence is silent about that case.

Does “either A or B” mean only one can happen?

Not by default. It guarantees at least one, so not A → B and not B → A. It means exactly one only when the passage rules out both, as with CLAT 2019's “the only computer in the room”. Check for that before you accept A → not B.