Question

Match the following:

$$\begin{array}{cc}\text{Column A}& \text{Column B}\\ \text{1. {x: x}\in \text{R, -5 < x}\le \text{15 }}& \text{a. 1}\\ \text{2. A =}\varphi \text{, then the power set P(A) has}\underset{–}{}\text{elements}& b.8\\ \text{3. Universal set of Rational Numbers}\&\text{Irrational Numbers}& c.\text{Real Numbers}\\ \text{4. No. of elements in Power Set of A}=\{a,b,c\}& d.\text{Integers}\\ & e.(-5,15]\\ & f.[-5,15)\end{array}$$

• A. 1 - b, 2 - a, 3 - c, 4 -e
• B. 1 - b, 2 - c, 3 - a, 4 -e
• C. 1 - e, 2 - a, 3 - c, 4 -b
• D. 1 - e, 2 - a, 3 - b, 4 -c

Answer 1

The correct option is C

1 - e, 2 - a, 3 - c, 4 -b

1. -5 < x ≤ 15 ⇒ (-5, 15]

2. ∅ is a subset of A, so, P(A) = {∅}

There is 1 element in P(A)

3. Universal set of rational and irrational numbers is real numbers.

4. A = {a, b, c}

P(A) has 2^n(A) elements

So, as n(A) = 3

No. of element in P(A) = 2³ = 8