Set Theory Model Questions Set 2 Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (b)

Set of natural numbers,

N = {1, 2, 3, 4, 5, 6, ...

(i) Addition: 2 + 3 = 5 is also an element of N.

(ii) Subtraction: 2 – 3 = –1 ∉ N

(iii) Multiplication: 2 × 3 = 6 ε N

(iv) Division: $3/2$. = 1.5 ∉ N (since, N contains only positive integers)

Therefore, the set of natural numbers is closed under addition and multiplication.

Answer: (d)

From figure,

(A ∩ B) ⊆ A (true)

(A ∩ B) ⊆ B (true)

and A ⊆ (A ∪ B) also (true)

Thus, all three statements are correct.

Shaded region = (A ∪ B).

Answer: (b)

LCM of 2, 3, 4, 5, 6 = 60

Number when divided by 2, 3, 4, 5, 6 gives

remainder 1, 2, 3, 4, 5 respectively here 2 – 1 = 1

3 – 2 = 1, 4 – 3, = 1, 5 – 4 = 1, 6 – 5 = 1

So required no. = 60 – 1 = 59

other no. 59 × 2 = 118

i.e. there is one no. below 100.

Answer: (d)

Given that

x ε {2, 3, 4}

and

y ε {4, 6, 9, 10}

A = x × y

But, A is set of pairs in which $1^{st}$ number is factor of second number.

A = {2, 3, 4} × {4, 6, 9, 10}

= {(2, 4); (2, 6); (2, 10); (3, 6); (3, 9); (4, 4)}

Total number of elements = 6

Answer: (b)

Percent of candidates, who failed in either Hindi or English

= (50 + 40 – 15)% = 75%

∴ Percent of candidates who passed in both subject

= 100 – 75 = 25%

Answer: (a)

Given, A = {1, 2, 3, 4}

So, the required subsets are {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}

and {1, 2, 3, 4}