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Let P be " Ananya is beautiful", and q be " Ananya is 165 cm tall" under what conditions is the statement, " Ananya is beautiful and 165 cms tall". true?

(A)

If Ananya is not beautiful and/or not 165 cm tall.

(B)

Only if Ananya is neither beautiful nor 165 cm tall.

(C)

Only if Ananya is both beautiful and 165 cm tall

(D)

If Ananya is beautiful and/or not 165 cm tall.

Question-2

Symbolise the statement " The square root of all prime numbers are irrational numbers" ( P → set of prime numbers, Q that of irrational numbers).

(A)

x Q : x = √x

(B)

x Q, x = √x

(C)

x P, √x Q

(D)

x P, √x Q.

Question-3

Write the statement ' Accountancy is a required subject for chartered Accountants (m) but not for engineers (n).

In symbolic form using the letter in parentheses to represent the corresponding component.

(A)

mΛ N

(B)

m V n

(C)

m ~ n

(D)

m Λ ~n

Question-4

Let P be " Shruti can type", and let q be " Shruti takes short hand". Write the statement ' Shruti can never type nor take short hand' in symbolic form.

(A)

pV q

(B)

PΛ~q

(C)

~PΛq

(D)

~ P Λ ~q

Question-5

Let P be " Ananya is beautiful", and q be " Ananya is 165 cms tall" under what conditions is the statement, " Ananya is beautiful or 165 cms tall". false?

(A)

If Ananya is not beautiful and / or not 165 tall

(B)

Only if Ananya is neither beautiful nor 165 cm tall

(C)

Only if Ananya is both beutiful and 165 cm tall

(D)

If Ananya is beutiful and /or not 165 cm tall.

Question-6

Let P be " Shruti can type", and let q be " Shruti takes short hand". Write the statement Shruti can type and take shorthand in symbolic form.

(A)

PΛ q

(B)

p V q

(C)

~ (p V q)

(D)

- P Λ - q

Question-7

Identify the quantifier in the statement " There exists a capital city for every state of India"

(A)

There exists

(B)

For every

(C)

Both a and b

(D)

None of these

Question-8

Write the contrapositive of the inverse of P q

(A)

pq

(B)

qp

(C)

~p~q

(D)

~q~p

Question-9

Write the statement. This is April (P) and income tax returns must be filed ( q) in symbolic form using the letter in

parentheses to represent the corresponding component

(A)

PVQ

(B)

P Q

(C)

PΛQ

(D)

P ~ Q

Question-10

A ______ is a sentence which is either true or false, but not both.

(A)

Statement

(B)

Converse statement

(C)

inverse statement

(D)

contrapositive

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