Question

The statement that is TRUE among the following?

Options

• The contrapositive of 3x + 2 = 8 ⇒ x = 2 is x ≠ 2 ⇒ 3x + 2 ≠ 8. 

• The converse of tanx = 0 ⇒ x = 0 is x ≠ 0 ⇒ tan x = 0.

• p ⇒ q is equivalent to pv ∼ q.

• p ∨ q and p ∧ q have the same truth table.

Answer 1

The contrapositive of 3x + 2 = 8 ⇒ x = 2 is x ≠ 2 ⇒ 3x + 2 ≠ 8. 

Explanation:

1. is true.
2. The converse of tanx = 0 `\implies` x = 0 is
   x = 0 `\implies` tan x = 0
   ∴ Statement (b) is false
3. ∼(P `\implies` q) is equivalent to p ∧∼q
   ∴ Statement given in option (c) is false.
4. No, p ∨ q and p ∧ q does not have the same truth value.