Question

Determinati multimea AnB, unde :
A = {x∈Z* | 21/2x+3 ∈ Z }
B = {x∈Z |15/2x+1 ∈Z }
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Answer 1

a) 2x+3∈D21
D21={1,3,7,21}
daca 2x+3=1⇒2x=1-3⇒2x=-2⇒x=-2/2⇒x=-1∈Z
daca 2x+3=3⇔2x=3-3⇔x=0∈Z
daca 2x+3=7⇒2x=7-3⇒x=4/2⇒x=2∈Z
daca 2x+3=21⇒2x=21-3⇒x=18/2⇒x=9∈Z
deci A={-1,0,2,9}
b) 2x+1∈D15
D15={1,3,5,15}
daca 2x+1=1⇒2x=1-1⇒x=0∈Z
daca 2x+1=3⇒2x=3-1⇒x=1∈Z
daca 2x+1=5⇒2x=5-1⇒x=2∈Z
daca 2x+1=15⇒2x=15-1⇒x=7∈Z
B={0,1,2,7}