It is given that if then , and if then not . Which of the following must be true?
Answer and explanation
Correct answer: B. If then not
- Step 1: Suppose is true. Then is true, and so cannot be true (because would make false). Hence .
- Step 2: None of the other statements can be derived from the two given implications.
Answer
If then not .
Why not the others: 'If then ' and 'if then ' reverse implications; 'both true' contradicts the facts; 'if not then ' is not forced since neither nor need be true.
Practise more Valid deductions.
Free questions with an explanation for every one, and full timed TMUA mock tests.
More Valid deductions questions
- It is given that if the sequence is geometric, then its ratio of consecutive terms is constant. It is also given that the ratio of consecuti…
- It is given that if is divisible by 12 then is divisible by 4, and that if is divisible by 4 then is even. Which of the foll…
- It is given that is positive or is a root of , and that is not positive. Which of the following must be true?
- It is given that if a positive integer is a perfect square then is divisible by 4 or is odd. It is also given that is not di…
- A function is such that: if is increasing, then ; and if is not increasing, then is not guarantee…
- It is given that is positive if and only if is positive, and that is not positive. Which of the following must be true?