Unit 1 [DS]

1.

2 points

Which is tautology? i)P v (~P → (Q v (Q → ~R ) ) ) ii)(~P Λ Q Λ R) v (P Λ Q)

only i

only ii

both i) and ii)

none of these

2.

2 points

Suppose 100 out of 120 CS students study at least one of the French(F),German(G) and Russian(R) language. 65 study F, 45 study G, 42 study R. 20 study F and G, 25 study F and R, 15 study G and R. Find the number of students who study only F and G but not R.

10

11

12

15

3.

1 point

Let P be "He is tall" and Q for "He is handsome".Then the statement "It is false that he is short or handsome" is:

P^Q

~(~P v Q)

P v ~Q

~P v Q

4.

1 point

If A and B are disjoint sets then-----------

A ∪ B=A

A∩B=A

A∪B =null set

A∩B= null set

5.

2 points

How many minimum disjunction symbols are required to represent P → Q in PDNF form

1

2

3

4

6.

2 points

The negation of ∀x{[C(x) ^ B(x)]→~P(x)} where C(x): x is an animal, B(x): x is a bird and P(x): x is a politician

∃x{[C(x) ^ B(x)] ^ P(x)}

∀x{[C(x) ^ B(x)]^ P(x)}

∃x{~[C(x) ^ B(x)]→P(x)}

∀x{~[C(x) ^ B(x)]→P(x)}

7.

2 points

Which of the statement is false?

set {a,b} is subset of {y,x,b,c,a}

For any set P, P is subset of P

set {a,b} is proper subset of {a,b}

sets can be combined in various ways to yield new sets

8.

1 point

If A and B are the two sets then which of the statements is true?

(A – B), (A∩B )and (B-A) are pair wise disjoint sets

(A – B) U (B-A)= A∩B

(A – B) ∩ (B-A)= A∩B

(A – B)U (B-A)= AUB

9.

2 points

If X and Y be the sets. Then the set " (X-Y) Union (Y-X) " is:

X Union Y

X intersection Y

(X Union Y) - (X intersection Y

none of these

10.

1 point

P→Q is equal to

P ^ ~Q

~P v ~Q

~P v Q

none of these

11.

1 point

If A and B are the two sets then which of the statements is true?

(A – B) and (B-A) are equal sets

(A – B) and (B-A) are disjoint sets

A - B=A

A - B= B

12.

2 points

Given two multisets, A={2.x,3.y,z} and B={4.x,2.a,3.b,2.z}, what is "A-B"?

{3.y}

{3.y,z}

{2.x}

none of these

13.

1 point

If D(x) represents "x is a Dog" and A(x) represents "x is an animal" then which is the symbolic form of the statement "if x is a dog then x is an animal"

A(x)→D(x)

A(x)↔D(x)

D(x)→A(x)

none of these

14.

2 points

Let P(x) denotes "x is a politician" then which is true? i)~∀xP(x)=∃x~P(x) ii)~∃xP(x)=∀x~P(x)

only i

only ii

both i) and ii)

none of these

15.

1 point

The dual of the statement P → Q is:

P → Q

Q → P

~P ^ Q

~P → ~Q

16.

1 point

{(P→Q↔(~P v Q)} ^ R is equal to

P

~P

Q

R

17.

2 points

How many minimum conjunction symbols are required to represent P → Q in PCNF form

1

2

3

none of these

18.

1 point

Which of the following is not well formed formula

(P v Q v R)

(P v Q)

(P → Q)

none of these

19.

2 points

Let C(x) denote "x is rose" and R(x) denote "x is red" then symbolize the expression "some roses are red"

∃x(C(x) ^ R(x))

∃x(C(x) → R(x))

both

none of these

20.

1 point

Which is tautology? i)P v ~(P^Q) ii)(P^Q) ^ ~(Q^P)

only i

only ii

both i) and ii)

none of these

21.

1 point

If A and B are the two sets then which of the statements is true?

A - B= {x|x ∈A and x ∈B}

A - B= {x|x ∈~A and x ∈B}

A - B= {x|x∈ A and x ∈~B}

A - B= {x|x ∈~A and x ∈~B}

22.

2 points

Consider two sets S1 and S2, where S1={J,M} and S2={{J,M}} then Which of the statements are true, i)J Є S1 ii)J Є S2 iii)S1 Є S2

i,iii

i,ii

i,ii,iii

only i

23.

2 points

P→(Q→R) is equal to

(~P^Q)→R

(P^~Q)→R

(~P^~Q)→R

(P^Q)→R

24.

2 points

Which of the statement is true? i)P → Q = ~P v Q ii)P → (Q V R) = (P → Q) V (P → R)

only i

only ii

both i) and ii)

none of these

25.

2 points

Let P(x) denotes "x can fly" and B(x) denotes "x is bird" then which is the correct representation of the statement "every bird can fly"

∀x(P(x)→B(x))

∀x(P(x)^B(x))

∀x(~B(x) v P(x))

none of these

26.

1 point

(P v Q v R) is

Dual

Well formed formula

both

none of these

27.

1 point

P v (P ^ Q) is equal to

P

Q

both

none of these

28.

1 point

(PvQ) v ~P is

Contradiction

Tautology

both

none of these

29.

1 point

How many elements will be there in power set of A, where A={1,2,3}

3

8

9

none of these

30.

1 point

Which is proposition? i) 2x3=5 ii)What is your name?

only i

only ii

both i) and ii)

none of these

31.

1 point

. If A={1,2,3,4,5 } and B={3,5,9,6,8} then A-B=--------------

{1,2,3,4,5,6,8,9}

{1,2,4,}

{9,6,8}

{3,5}

32.

1 point

How many elements will be there in power set of A, where A={a,b,c,d}

4

8

15

16

33.

2 points

Which is true if G stands for "is greater than" i)G(x,y) is 2 palce predicate ii)G(x,y) means "x is greater than y"

only i

only ii

both i) and ii)

none of these

34.

2 points

{~P ^ (~Q ^ R)} v (Q^R) v (P^R) is equal to

P

Q

R

none of these

35.

1 point

If S is a set containing n number of elements then number of elements in power set of s, i.e. P(s) are.

2n

n2

n

2n

36.

2 points

Among the integers 1 to 300, how many of them are not divisible by 3, nor by 5, nor by 7 ?

102

138

140

162

37.

1 point

For sets A and B, (A∩B)UA=

A

B

AUB

Depends on the sets

38.

1 point

P ^ (P v Q) is equal to

P

Q

both

none of these

39.

2 points

Which of the statement is false? i)The intersection of {a,b} and {a,c} is set which contain 1 element ii)Power set of empty set contain 1 element iii)Set {a,b} and {c,d} are disjoint sets

only i

i,ii

all of these

none of these

40.

1 point

How many elements will be there in set obtained from {a,b,c}-{a} where - stands for difference of 2 sets

0

1

2

3