Math

QuestionWhich sets are equal? A. E=FE=F C. A=CA=C E. J=LJ=L B. A=BA=B D. E=HE=H F. C=DC=D with sets A,B,C,D,E,F,J,LA, B, C, D, E, F, J, L.

Studdy Solution

STEP 1

Assumptions1. The sets are given as follows - A={a,e,j,k}A=\{a, e, j, k\} - B={x,y,z,}B=\{x, y, z,\} - C={j,k,e,a}C=\{j, k, e, a\} - =\1 \leq x \leq4 \text { and } x \in \mathbb{}\} - ==\varnothing - ={}=\{\varnothing\} - G={0}G=\{0\} - H={}H=\{ \} - J={xx=4n+5 and nW}J=\{x \mid x=4 n+5 \text { and } n \in W\} - ={xx=4n5 and n}=\{x \mid x=4 n-5 \text { and } n \in \mathbb{}\}. Two sets are equal if and only if they contain exactly the same elements.

STEP 2

We will compare each pair of sets given in the options.
A. =F=F
istheemptyset,whichmeansitcontainsnoelements. is the empty set, which means it contains no elements. is a set that contains the empty set as its only element. Therefore, F \neq F.

STEP 3

B. A=BA=B
AA contains the elements a,e,j,ka, e, j, k and BB contains the elements x,y,z,wx, y, z, w. These are different elements, so ABA \neq B.

STEP 4

C. A=CA=C
AA contains the elements a,e,j,ka, e, j, k and CC contains the elements j,k,e,aj, k, e, a. Even though the order is different, they contain the same elements. Therefore, A=CA = C.

STEP 5

. =H=H
Both $$ and $H$ are empty sets, which means they contain no elements. Therefore, $ = H$.

STEP 6

. J=LJ=L
JJ contains all numbers of the form 4n+54n+5 where nn is a whole number. $$ contains all numbers of the form $4n-5$ where $n$ is a natural number. These are different forms, so $J \neq L$.

STEP 7

. C=DC=D
CC contains the elements j,k,e,aj, k, e, a and $$ contains all numbers between1 and4 (inclusive) that are natural numbers. These are different elements, so $C \neq D$.
So, the sets that are equal are A=CA=C and =H=H.

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