Question

Which of the following is/are equal sets?

• A. A = Set of prime numbers less than 6 B = set of prime factors of 30
• B. A = {x: x - 5 = 0} B = {x: x is a positive integral root of the equation $x^2$-2x-15=0 }
• C. A = {x: x is even integer and x ≤ 10} B = {2, 4, 6, 8, 10}
• D. A = {x: x is a letter in the word FELLOW} B = {y: y is a letter in the word WOLF}

Answer 1

Answer: (A), (B)

A = {x: x - 5 = 0}

B = {x: x is a positive integral root of the equation $x^2$-2x-15=0 }

$\text{(a)}A=\text{Set of prime numbers less than}6=\{2,3,5\}$

$B=\text{Set of prime factors of}30=\{2,3,5\}$
Hence A, B are equal sets in option (a)

$\text{(b)}A=\left\{5\right\}$

If $x^2-2x-15=0$
$\Rightarrow x=5,-3$

and $B=\{x:x\text{is a positive integral root of the equation}{x}^2-2x-15=0\}=\left\{5\right\}$

Hence $A,B$ are equal sets in option (b)

(c) $A=\{x:x\text{is even integer and}x\le 10\}=\{---,-4,-2,0,2,4,6,8,10\}$
$B=\{2,4,6,8,10\}$
Here $A\ne B$

(d) A = {E, F, O, L, W}

B = {F, O, L, W}

So, A $\ne$ B

So, options (a) & (b) gives equal sets.