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If statement (P →q) → (q →r) is false, then truth values of statements p,q and r respectively can be
- a)FTF
- b)TTT
- c)FFF
- d)FTT
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If statement (P→q)→(q→r) is false, then truth values of...
If (P →q) →(q →r) is false then (p →q) must be true and (q →r) must be false.
Now,
If P →q is true then P & q both can be true or false :
If q →r is false then q must be true and r must be false
So when both condition i.e. P →q true and q → r false satisfy then q is true, r is false and P can be true or false
Now,
If P →q is true then P & q both can be true or false :
If q →r is false then q must be true and r must be false
So when both condition i.e. P →q true and q → r false satisfy then q is true, r is false and P can be true or false
Most Upvoted Answer
If statement (P→q)→(q→r) is false, then truth values of...
Understanding the Statement
To determine when the statement (P→Q)→(Q→R) is false, we need to analyze the truth table of the involved variables.
Truth Table Basics
1. The conditional statement A→B is false only when A is true and B is false.
2. Therefore, (P→Q) is false when P is true and Q is false.
3. The statement (Q→R) is false when Q is true and R is false.
Analyzing the Implication
The entire expression (P→Q)→(Q→R) is false in the following scenario:
- P is true (T)
- Q is false (F)
- When Q is false, (Q→R) becomes true regardless of R's value.
Thus, the implication (P→Q)→(Q→R) can only be false if:
- (P→Q) is true, and (Q→R) is false.
- For (Q→R) to be false, Q must be true and R must be false, which contradicts Q being false.
Finding the Right Combination
Now, let's evaluate the combinations:
- Option a: F T F:
- P = F, Q = T, R = F
- (P→Q) = T (because F→T is T)
- (Q→R) = F (because T→F is F)
- Thus, (P→Q)→(Q→R) = T→F = F (this is a valid scenario)
- Option b: T T T:
- This results in the expression being true.
- Option c: F F F:
- This results in the expression being true.
- Option d: F T T:
- This also results in the expression being true.
Conclusion
The only combination that makes the expression (P→Q)→(Q→R) false is when P is false, Q is true, and R is false. Therefore, the correct answer is:
Option A: F T F
To determine when the statement (P→Q)→(Q→R) is false, we need to analyze the truth table of the involved variables.
Truth Table Basics
1. The conditional statement A→B is false only when A is true and B is false.
2. Therefore, (P→Q) is false when P is true and Q is false.
3. The statement (Q→R) is false when Q is true and R is false.
Analyzing the Implication
The entire expression (P→Q)→(Q→R) is false in the following scenario:
- P is true (T)
- Q is false (F)
- When Q is false, (Q→R) becomes true regardless of R's value.
Thus, the implication (P→Q)→(Q→R) can only be false if:
- (P→Q) is true, and (Q→R) is false.
- For (Q→R) to be false, Q must be true and R must be false, which contradicts Q being false.
Finding the Right Combination
Now, let's evaluate the combinations:
- Option a: F T F:
- P = F, Q = T, R = F
- (P→Q) = T (because F→T is T)
- (Q→R) = F (because T→F is F)
- Thus, (P→Q)→(Q→R) = T→F = F (this is a valid scenario)
- Option b: T T T:
- This results in the expression being true.
- Option c: F F F:
- This results in the expression being true.
- Option d: F T T:
- This also results in the expression being true.
Conclusion
The only combination that makes the expression (P→Q)→(Q→R) false is when P is false, Q is true, and R is false. Therefore, the correct answer is:
Option A: F T F
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If statement (P→q)→(q→r) is false, then truth values of statements p,q and r respectively can bea)FTFb)TTTc)FFFd)FTTCorrect answer is option 'A'. Can you explain this answer?
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If statement (P→q)→(q→r) is false, then truth values of statements p,q and r respectively can bea)FTFb)TTTc)FFFd)FTTCorrect answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If statement (P→q)→(q→r) is false, then truth values of statements p,q and r respectively can bea)FTFb)TTTc)FFFd)FTTCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If statement (P→q)→(q→r) is false, then truth values of statements p,q and r respectively can bea)FTFb)TTTc)FFFd)FTTCorrect answer is option 'A'. Can you explain this answer?.
If statement (P→q)→(q→r) is false, then truth values of statements p,q and r respectively can bea)FTFb)TTTc)FFFd)FTTCorrect answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If statement (P→q)→(q→r) is false, then truth values of statements p,q and r respectively can bea)FTFb)TTTc)FFFd)FTTCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If statement (P→q)→(q→r) is false, then truth values of statements p,q and r respectively can bea)FTFb)TTTc)FFFd)FTTCorrect answer is option 'A'. Can you explain this answer?.
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