Question

Answer this question ​

Answer 1

$\Large\boxed {A\cap B=\phi}$

Consider,

$A=\{\mathrm {x}:\text {x is the}\ \mathrm {4^{th}}\ \text {term of the AP}\ \mathrm {10,\ 6,\ 2,\dots}\}$

Well, the 4th term of the AP means that A is a singleton set, because 4th term is only of one term.

The 4th term of the AP is 10 + 3(6 - 10) = -2.

Thus,

$A=\{-2\}$

Consider,

$B=\{\mathrm {x}:\text{x is a solution of}\ \mathrm {x^2-4=0,\ x\in\mathbb {N}}\}$

First let me solve the quadratic equation,

x² - 4 = 0

(x - 2)(x + 2) = 0

=> x = 2 ; x = -2

But 2 is a natural number, not -2. Then,

x = 2.

Thus,

$B=\{2\}$

Since A and B are disjoint,

$\largeA\cap B=\phi$

#answerwithquality

#BAL