Question

If q is false and p ∧ q `leftrightarrow` r is true, then which one of the following statements is a tautology?

विकल्प

• (p ∨ r) `rightarrow` (p ∧ r)

• (p ∧ r) `rightarrow` (p ∨ r)

• p ∧ r

• p ∨ r

Answer 1

`bb((p ∧ r) rightarrow (p ∨ r))`

Explanation:

q is false and [(p ∧ q) `leftrightarrow` r] is true

As (p ∧ q) is false

[False `leftrightarrow` r] is true.

Hence r is false

Option (a): says p ∨ r, Since r is false

Hence (p ∨ r) can either be true or false

Option (b): says (p ∧ r) `rightarrow` (p ∨ r) (p ∧ r) is false

Since, F `rightarrow` T is true and 

F `rightarrow` F is also true.

Hence, it is a tautology

Option (c): (p ∨ r) `rightarrow` (p ∧ r)

i.e. (p ∨ r) `rightarrow` F

It can either be true or false

Option (d): (p ∧ r), Since, r is false

Hence, (p ∧ r) is false.