Let Z be the set of integers. If A = { x in Z | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given $A = \{ x \in Z : 2^{(x + 2)(x^2 - 5x + 6)} = 1 \}$.Since $2^0 = 1$,we have $(x + 2)(x^2 - 5x + 6) = 0$.Factoring the quadratic: $(x + 2)(x

Vedclass · Accepted Answer

$2^{15}$

Vedclass · Answer

(A) Given $A = \{ x \in Z : 2^{(x + 2)(x^2 - 5x + 6)} = 1 \}$.Since $2^0 = 1$,we have $(x + 2)(x^2 - 5x + 6) = 0$.Factoring the quadratic: $(x + 2)(x - 2)(x - 3) = 0$.Thus,$x = -2, 2, 3$. So,$A = \{ -2, 2, 3 \}$ and $n(A) = 3$.Given $B = \{ x \in Z : -3 Adding $1$ to all parts: $-2 Dividing by $2$: $-1 Since $x \in Z$,$B = \{ 0, 1, 2, 3, 4 \}$ and $n(B) = 5$.The number of elements in $A 	imes B$ is $n(A) 	imes n(B) = 3 	imes 5 = 15$.The number of subsets of a set with $n$ elements is $2^n$.Therefore,the number of subsets of $A 	imes B$ is $2^{15}$.

Let $Z$ be the set of integers. If $A = \{ x \in Z : 2^{(x + 2)(x^2 - 5x + 6)} = 1 \}$ and $B = \{ x \in Z : -3 < 2x - 1 < 9 \}$,then the number of subsets of the set $A \times B$ is:

Similar Questions

Domain of $f(x) = \log |\log x|$ is

$A$ survey shows that $73 \%$ of the persons working in an office like coffee,whereas $65 \%$ like tea. If $x$ denotes the percentage of them who like both coffee and tea,then $x$ cannot be

If $A = \{1, 2, 3, 4, ..., 100\}$ and $B = \{51, 52, 53, ..., 180\}$,then the number of elements in $(A \times B) \cap (B \times A)$ is:

Find the cardinal number of the following set $\{x: x\}$ is a natural number $\leq 30$ and is divisible by $7$ or $\{11\}$

If $A = \{a, d\}, B = \{b, c, e\}$ and $C = \{b, c, f\},$ then $A \times (B - C) =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module