If p : A man is happy
q : A man is rich
Then, the statement, " If a man is not happy, then he is not rich " is written as
~ p → ~ q
~ q → p
~ q → ~ p
q → ~ p
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
~ p Λ q is logically equivalent to
p → q
q → p
~ ( p → q)
~ ( q → p)
Which of the following is the inverse of the proposition : " If a number is a prime, then it is odd" ?
If a number is not a prime, then it is odd
If a number is not a prime, then it is not odd
If a number is not odd, then it is not a prime
If a number is odd, then it is a prime
Let S be a non-empty subset of R. Consider the following statement
P : There is a rational number x S such that x > o.
Which of the following statements in the negation of the statement P
There is a rational number x S such that x ≤ o
There is no rational number x S such that x ≤ o
Every rational number x S satisfies x ≤ o
x S and x ≤ o x is not rational
~ ( p q) (~ p Λ q) is logically equivalent to
~ p
p
q
~ q
Identify the false statement
~ [p ( ~ q) ] Ξ ( ~ p) Λ q
[ p q] ( ~ p) is a tautology
[p Λ q] Λ ( ~ p) is a contradiction
~ (p q) Ξ ( ~ p) ( ~ q)
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 negation of the proposition " If 2 is prime, then 3 is odd " is
if 2 is not prime, then 3 is not odd
2 is prime and 3 is not odd
2 is not prime and 3 is odd
if 2 is not prime, then 3 is odd
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)
