Maths · Relations, type of relations, equivalence relations
Consider the following two statements: If 7 is an odd number, then 7 is divisibl
Consider the following two statements: \( P: \) If 7 is an odd number, then 7 is divisible by 2. Q: If 7 is a prime number, then 7 is an odd number If \( V_{1} \) is the truth value of the contrapositive of \( \mathrm{P} \) and \( V_{2} \) is the truth value of contrapositive of \( Q, \) then the ordered pair \( \left(V_{1}, V_{2}\right) \) equals:
- A. \( (F, F) \)
- B. \( (T, T) \)
- C. \( (T, F) \)
- D. \( (F, T) \)
Step-by-step solution
Statement P: 'If 7 is odd then 7 is divisible by 2' is false (true implies false). Its contrapositive 'If 7 is not divisible by 2 then 7 is not odd' is also false (true implies false). So V1 = F. Statement Q: 'If 7 is prime then 7 is odd' is true (true implies true). Its contrapositive 'If 7 is not odd then 7 is not prime' is true (false implies false). So V2 = T. Thus (V1, V2) = (F, T).
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