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Question Bank No: 1

1. A statement among the following is,

a)		Every rectangle is a parallelogram
b)		Who is the father of geometry?
c)		Is 1a a prime number?
d)		Sit down.

2. Of the following, the one which is not a statement is,

a)		2+3=4
b)		Moon revolves around the sun
c)		6 has four different prime factors
d)		Read the question carefully.

3. A statement with truth value F is ,

a)		Between two distinct rational numbers, there are infinitely many irrational numbers.
b)		Every nonempty finite set of integers contains a smallest number
c)		Every non-empty set of real numbers contains a smallest number.
d)		every non-empty finite set of integers contains a smallest number.

4. The statement with truth value T is,

a)		A prime number greater than 100 is odd
b)		The intersection of two nonempty sets is none mpty
c)		Between two distinct natural numbers, there is a natural number.
d)		4 is aprime number

5. If p and q are two statements, then a statement with truth value T is,

a)		p $\lor$ q
b)		p $\land$ q
c)		p $\lor \sim$ q
d)		q $\lor \sim$ q

6. If p and q have truth value T and r has truth value F, then,

a)		(p $\lor$ r) $\land$ q has truth value F
b)		(q $\lor$ r) $\land$ p has truth value F
c)		(p $\land$ q) $\lor$ r has truth value T
d)		None of these

7. If the truth value of p and q are T and F respectively then,

a)		$\sim (p \lor \sim q)$ has truth value T
b)		$\sim (p \land \sim q)$ has truth value F
c)		(p $\land q)$ $\lor$ (p $\land \sim q)$ has truth value T
d)		None of these

8. Each of the statements p $\to$ q. q $\to$ r and ~ r is true, then

a)		p is true
b)		p is flase
c)		q is true
d)		none of these.

9. If p,q are two statements , then

a)		~(p $\land$ q) = ~p $\land$ ~q
b)		~(p $\lor$ q) = ~p $\lor$ ~q
c)		~(p $\to$ q) = p $\land$ q
d)		~(p $\to$ q) =p $\land$ ~q

10. If p,q,r, are statements such that p $\equiv$ ~q and r $\equiv$ ~s, then (p $\lor$ r) $\land$ (q $\land$ s) =

a)		t
b)		c
c)		p $\lor$ s
d)		p $\land$ r

11. The truth value of the following two statements
1. "Complex numbers are real numbers if and only if all squares are rectangles"
2. " Hydrogen is a gas if and only if iron is not a metal" are respectively"

a)		F,F
b)		F,T
c)		T,T
d)		T,F

12. Which of the following is not true ? The conditionla statements p $\to$ q means

a)		if p then q
b)		q if p
c)		p only if q
d)		q is necessary for p

13. The negation of p $\leftrightarrow$ q is

a)		(~p $\lor$ q) $\land$ (~q $\lor$ p)
b)		(~p $\lor$ q) $\lor$ (~q $\lor$ p)
c)		(~p $\land$ q) $\land$ (~q $\land$ p)
d)		(~p $\land$ q) $\lor$ (~q $\land$ p)

14. The dual of the statement p $\land$ ~ p = c is

a)		p $\lor$ ~p = c
b)		p $\land$ ~p = t
c)		p $\lor$ ~p = t
d)		p $\land$ ~p = c

15. Each of the statments p $\to \sim$ q,~r $\to$ q and p is true. Then

a)		r is false
b)		r is true
c)		q is true
d)		p $\land$ q is true

16. p $\land \sim$ q) $\land$ (~p $\land$ q) is,

a)		a tautology
b)		a contradiction
c)		both tautology and contradiction
d)		neither a tautology nor a contradiction

17. If p is the statement '0' is a natural number' and q is the statement '5 is factor of 10' , then

a)		p $\to \sim$ q and ~p $\to$ q have truth values T
b)		p $\to \sim$ q has truth value T and ~p $\to$ q has truth value F
c)		~p $\leftrightarrow$ ~q has truth value F
d)		p $\leftrightarrow \sim$ q has truth value T

18. If p $\to$ (~p $\lor$ q) is false, the truth values of p and q are respectively,

a)		F,T
b)		F,F
c)		T,T
d)		T,F

19. $D_{6}$ ={1,2,3,6} is a Boolean Algebra w.r.t the operations a+b = lcm of a and b, a.b = gcd of a and b and a' = $\frac{6}{a}$ $\forall$ a, b $\in$ $D_{6}$ The multiplicative identity elements is

a)		1
b)		2
c)		4
d)		6

20. The additive element of the Boolean Algebra of logical statements is

a)		t
b)		f
c)		0
d)		none of these

21. Let X be a nonempty setP(X) = {A: A $\subset$ X} is Boolean Algebra w.r.t. the operations A+B = A $\cup$ B, A.B = A $\cap$ B A' = X - A $\forall$ A, B $\in$ P (X)The additive identity element is

a)		X
b)		$φ$
c)		{ $φ$ }
d)		{X}

22. In a Boolean algeobra a'.b' =

a)		(a+b)'
b)		(a.b)'
c)		(a'.b')'
d)		a+b

23. In a Boolean algebra, a is not equal to

a)		a.a
b)		a+a
c)		a+a.b
d)		(a'.b')'

24. If B is a Boolean algebra and a,b,c $\in$ B then a + (b,c) =

a)		(a+b).c
b)		a.c +b.c
c)		(a+b).(a+c)
d)		a

25. If a,b,c $\in$ B then a+b+a'.b' =

a)		0
b)		1
c)		a'+b'
d)		a+b

26. If a,b,c, $\in$ B then a.b +c.(a'+b') =

a)		a+b.c
b)		a.b+c
c)		(a.c+b)
d)		(a+b).c

27. In a Boolean algebra B, a.b+a.b'+a' =

a)		a
b)		b
c)		0
d)		1

28. In a Boolean algebra a'+b = 1 then

a)		a=b
b)		a=0
c)		a+b = 0
d)		a.b' = 1

29. In a Boolean algebra (a+b)' + (a'+b')' =

a)		a
b)		b
c)		a'
d)		b'

30. In a Boolean algebra a.b+[(a+b').b]' =

a)		a
b)		b
c)		1
d)		0

31. If x,y $\in$ B ( a Boolean algebra) then the dual of the statement x+[y'+x).y]'=1

a)		x'+(y+x').y' = 0
b)		x.[(y'.x) + y]' = 0
c)		x'.((y.x') + y') = 0
d)		None of these

32. In a Boolean algebra the dual of the statement x.y'+y = x+y is

a)		x'.y + y' = x'+y'
b)		x'+y.y' = x'.y'
c)		(x+y').y = x'.y'
d)		(x+y').y = x.y

33. In a Boolean algebra x.y.z + x.y'.z' is equal to

a)		x.(y.z')'
b)		x.(y'.z)'
c)		x.(y'+z)
d)		x.y.z

34. The value of the Boolean expression (x.y + x'.z). (x+y.z) in the Boolean algebra of switching circuits is =

a)		1 if x = 1, y = 1, z= 1
b)		if x = 1, y = 0 z= 0
c)		if x = 0, y = 0, z= 1
d)		if x = 1, y = 0, z= 1

35. The Boolean polynomial representing the circuitis
q11-35 Can be simplified to

a)		(a+c.b').(b+c')
b)		a.(c+b')+b.c'
c)		a.(c+b').(b+c')
d)		(a+b+c').(c+b')

36. The Boolean polynomial representing the circuit
q11-36 is

a)		p.q + (q'+r') + p'.r
b)		(p+q).(q.r').(p'+r)
c)		p.q+q'.r'+p'.r
d)		p+q+q'+r'+p'+r

37. If a,b, $\in$ B then a+a.b =

a)		a+b
b)		a.b
c)		a
d)		b

38. Boolean expression corresponding to the following combinatorial circuit is
q11-38 equal to

a)		( $x_{1}$ . $x_{2}$ ). $(x_{1}^{'} . x_{2})$
b)		$(x_{1} . x_{2})$ $(x_{2}^{'} . x_{2})$
c)		$(x_{1} x_{2})$ . $({x'}_{1} + x_{2})$
d)		all the above

39. The Boolean function of the combinatorial gate
q11-39 is

a)		f(x,y,z) = ( x'+y').z
b)		f(x,y,z) = (x.y)' + z
c)		f(x,y,z) = (x.y) +z'
d)		f(x,y,z)=(x+y)'.z

40. The Boolean expression for the output of the logic circuit
q11-40

a)		(x+y)'+x
b)		(x.y)'+x
c)		(x.y)'.x
d)		d'.y'+x

41. If x,y, z are three elements of a Boolean algebra then (x+y).(y+z).(z+x) =

a)		2x.y.z
b)		x.y+y.z+z.x
c)		(x+y+z $)^{2}$
d)		x+y+z

42. 42.The circuit(p.q')+(p.q.r)+ (p'.r) is equal to

a)		(p+r).r
b)		(p'+q).r
c)		(p'+q').r
d)		(p.q')+r

43. If x,y are any two element of a Boolean algebra, then (x+y).(x+y').(x'+y) is equal to

a)		x+y
b)		x.y
c)		x'+y
d)		x.y'

44. The Boolean expression corresponding to the combinatorial circuit
q11-44 can be simplified to

a)		$x_{2}$
b)		$x_{1} +$ ${x'}_{2}$
c)		${x'}_{1}$ + $x_{2}$
d)		$x_{1}$ + $x_{2}$

45. The circuit A.(B+C).B. (b+C') is equivalent to

a)		A.B.C'
b)		A.C'
c)		A.B'
d)		AB

46. The switching circuit (A+C).(A'+B)+C.(B'+C') is equivalent to

a)		A.B+C
b)		A.C+B
c)		B.C+A
d)		A+B+C

47. The circuit (A+B).(B'+C)+(B+C).(A'+C') is equivalent to

a)		A.B+C
b)		A.C+B
c)		B.C+A
d)		A+B+C

48. In a Boolean algebra a.b.c' + a.b'.c+a.b'.c' =

a)		a.b.c'
b)		a.(b+c)
c)		a.(b'+c')
d)		a.(b+c')

49. There is no Boolean algebra containing exactly n elements where

a)		n = 2
b)		n = 3
c)		n= 4
d)		n= 8

50. The number of possible switching circuits with three switches is

a)		2
b)		3
c)		4
d)		5