# 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**

**a)** Contradiction

**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)

Answers