If S ( p,q,r) = ( ˜ p) [ ˜ ( q Λ r) ] is a compound statement, then S ( ˜ p, ˜ q, ˜ r ) is
˜ S ( p,q,r)
S ( p,q,r)
p (q Λ r)
p (q r)
The negation of the statement " he is rich and happy " is given by
he is not rich and not happy
he is not rich or not happy
he is rich and happy
he is not rich and happy
Which of the following statements is a tautology?
( ~ q Λ p ) Λ q
( ~ q Λ p ) Λ ( p Λ ~ p)
( ~ q Λ p ) ( p ~ p)
( p Λ q) Λ ( ~ (p Λq))
Let p be the statement 'Ravi races' and let q be the statement 'Ravi wins'. Then, the verbal translation of ~ ( p ( ~ q)) is
Ravi does not race and Ravi does not win
It is not true that Ravi races and that Ravi does not win
Ravi does not race and Ravi wins
It is not true that Ravi races or that Ravi does not win
Which of the following statement has the truth value 'F' ?
A quadratic equation has always a real root
The number of ways of seating 2 persons in two chairs out of n persons is P ( n, 2)
The cube roots of unity are in GP
None of the above
The contrapositive of ( p q) → r is
~ r → ( p q)
r → ( p q )
~ r → ( ~ p Λ ~ q)
p→ ( q r )
Statement 1 ~ ( p ↔ ~ q) is equivalent to p ↔ q .
Statement II ~ ( p ↔ ~ q) is a tautology.
Statement 1 is true, Statement II is true; Statement II is a correct explanation for Statement 1.
Statement 1 is true, Statement II is true; Statement II is not a correct explanation for Statement 1.
Statement 1 is true, Statement II is false.
Statement 1 is false , Statement II is true.
Let p ans q be two statements, then ( p q ) ~ p is
tautology
contradiction
Both (a) and (b)
None of these
~ ( p q) (~ p Λ q) is logically equivalent to
~ p
p
q
~ q
~ p Λ q is logically equivalent to
p → q
q → p
~ ( p → q)
~ ( q → p)
