teorema de pitagoras a=(x-1) b=(1,3)
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Class 11
>>Applied Mathematics
>>Relations
>>Cartesian product of sets
>>Let A = { x ∈ W : x < 2 }, B = x ∈ N :
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Let A={x∈W:x<2},B=x∈N:1<x≤4} and C={3,5}. Verify that :
A×(B∪C)=(A×B)∪(A×C)
Medium
Updated on : 2022-09-05
Solution
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A={0,1},B={2,3,4} and C={3,5}
∪ is combination of two sets.
B∪C={2,3,4,5}
Now,
L.H.S=A×(B∪C)
={0,1}×(2,3,4,5}
={(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)} ---- ( 1 )
R.H.S=(A×B)∪(A×C)
={0,1}×{2,3,4}∪{0,1}×{3,5}
={(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)}∪{(0,3),(0,5),(1,3),(1,5)}
={(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)} ---- ( 2 )
From ( 1 ) and ( 2 )
⇒ L.H.S=R.H.S
∴ A×(B∪C)=(A×B)∪(A×C)