# Mathematical Logic & Boolean Algebra MCQs

1) The statement ~ (p q) is equivalent to
a) P (~ q)
b) ~ p q
c) p q
d) ~ p ~ q

2) Let f denote the Boolean function for the circuit given below Then f has as expression
a)
b)
c)
d)

3) Let p be the statement ‘Ravi races’ and let Q be the statement ‘Ravi wins’. Then the verbal translation of ~ ( p ( ~ Q ) ) is
a) Ravi does not race and Ravi does not win
b) It is not true that Ravi races and that Ravi does not win
c) Ravi does not race or Ravi wins
d) It is not true that Ravi races or that Ravi does not win

4) Let B be a Boolean algebra. If is equal to
a)
b)
c)
d)

5) The output of the circuit is
a)
b)
c)
d)

6) Identify the false statement
a)
b) is a tautology
c) [p q] (~ p)
d) ~( p q) (~ p) (~q)

7) If p and q are statements which of the following is a tautology.
a) p ~ p
b) p ~ p
c) p q
d) p q

8) If p and q are statements, then (~ p q ) ( p ( ~q)) is a
b) Tautology
c) Compound statement
d) None of these.

9) Which of the following is logically equivalent to the statement p q.
a) p ~q
b) ~p q.
c) ~ p ~q
d) None of these

10) ~ (p q)
a) p ~ q
b) ~ p q
c) p ~q
d) ~ p q

11) If p : n is a natural number ; q : n – 1 is a natural number, which of the following is a true statement.
a) p q
b) q p
c) p q
d) None of these

12) If p: All rational numbers are real numbers, then which of the following is not equivalent to the negation of p.
a) All rational numbers are not real numbers.
b) Not all rational numbers are real numbers
c) It is not true that rational numbers are real numbers
d) There are rational numbers which are not real numbers.

13) ~ (p q)
a) ~p ~ q
b) ~ p q
c) p ~q
d) ~ p ~ q

14) The dual of the statement of (p q) t
a) (p q) c
b) (p q) t
c) (p q) c
d) (p q) t

15) If p: 4 + 3 = 7 ; q: 4 x 3 = 7, then which of the following compound statement has the truth value T
a) p q
b) q p
c) p q
d) ~ p q

16) If p, q, r, s are logical statements such that p ~ q, r ~s, then (p r) (q s)
a) t
b) c
c) p r
d) p r

17) If p: 4 is an even number , q: 6 is a divisor of 12 and r: the HCF of 4 and 6 is 2 , then which one of the following is true
a) p q (p q) t
b) (p q) ~r
c) ~(q r) p
d) ~p (q r)

18) Which of the follpwing is not true for any two statements p and q.
a) ~[ p ~q] ~p q
b) (p q) (~ q) is a tautology
c) ~ [ p ~ p] is a tautology
d) ~( p q) (~ p) (~ q)

19) The output of the circuit is
a)
b)
c)
d)

20) In a Boolean algebra B with respect to ‘+’ and ‘.’ , denotes the negation of x B then
a)
b)
c)
d)

21) The Boolean expression corresponding to the combinatorial circuit is
a)
b)
c)
d)

22) The statement ~ (p q) is equivalent to
a) p q
b) ~ p ~q
c) p q
d) ~ p ~ q

23) The dual of the statement (p q) r is
a) (p q) r
b) (p q) r
c) (p q) r
d) None of these

24) The dual of the statement (p q) t if t denotes tautology and c denotes contradiction
a) (p q) t
b) (p q) c
c) (p q) t
d) None of these

25) The dual of the statement (p c) r if t denotes tautology and c denotes contradiction
a) (p t) r
b) (p c) r
c) (p t) r
d) None of these

26) ~ (~p q)
a) (~p q)
b) (p ~q)
c) (p ~q)
d) (p q)