Decide whether given sets are equal sets. Give reasons: A {x/x = 3n,n €N, 0<x<15}
B = { y/ y is a number that gives remainder zero when divided by 3, 1≤ ≤ 15}
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Answer:
(i) A={2,3}
B={x:x is a solution of x
2
+5x+6=0}
x
2
+5x+6=0
x(x+3)+2(x+3)=0
(x+2)(x+3)=0
x=−2 or x=−3
∴B={−2,−3}
∴A
=B
(ii) A={x:x is a letter in the word FOLLOW}={F,O,L,W}
B={y:y is a letter in the word WOLF}={W,O,L,F}
The order in which the elements of a set are listed is not significant.
∴A=B
Step-by-step explanation:
(i) A={2,3}
B={x:x is a solution of x
2
+5x+6=0}
x
2
+5x+6=0
x(x+3)+2(x+3)=0
(x+2)(x+3)=0
x=−2 or x=−3
∴B={−2,−3}
∴A
=B
(ii) A={x:x is a letter in the word FOLLOW}={F,O,L,W}
B={y:y is a letter in the word WOLF}={W,O,L,F}
The order in which the elements of a set are listed is not significant.
∴A=B
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