Set Theory Model Questions Set 2 Practice Questions Answers Test with Solutions & More Shortcuts

Answer: (d)

Number of people who do not read any of these newspaper = total population – number of people who read atleast one of these newspapers.

number of people who read atleast one of these newspapers = 1% + 1% + 3% + 1% + 7% + 19% = 32% of total population = 32000

required number of people = 100000 – 32000 = 68000

Answer: (a)

Given, A ≡ $x^2$ – 6x + 8 = 0

⇒ (x – 4) (x – 2) = 0

⇒ x = 4, 2

and B ≡ $2x^2$ + 3x – 2 = 0

⇒ (2x – 1) (x + 2) = 0

⇒ x = $1/2$ , –2

Hence, neither A ⊆ B nor B ⊆ A.

Answer: (b)

Here, {Φ} is an element of {Φ} ε {{Φ}, {{Φ}}}.

Answer: (b)

Solving the given equation for x, we have

x + 5 = 5 ⇒ x = 5 – 5 = 0

Therefore, in the given set we have only one element i.e. 0. Element Φ is a null set i.e. no elements in the set.

Hence, option (b) is the correct answer.

Answer: (c)

We know that

A ∩ (B ∪ C) = {A ∩ B) ∪ (A ∩ C)

Example:

A = Set of an even natural number

A = {2, 4, 6, 8, 10, 12, ...}

B = Set of natural number and multiples of 5.

B = {5, 10, 15, 20, 25, ...}

C = Set of natural number and multiple of 10.

C = {10, 20, 30, 40, 50, ...}

A ∩ B = {2, 4, 6, 8, 10, 12, ...} ∩ {5, 10, 15, 20, 25, ...} = {10, 20, 30, ...}

A ∩ C = {2, 4, 6, 8, 10, 12, ...} ∩ {10, 20, 30, 40, 50, ...} = {10, 20, 30, 40, ...}

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

= {10, 20, 30, ...} ∪ {10, 20, 30, 40, ...}

= {10, 20, 30, 40, ...}