5/3 x 3/5 =___
a)1 b)0 c)-1
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Class 11
>>Applied Mathematics
>>Relations
>>Cartesian product of sets
>>Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5
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Let A={1,2},B={1,2,3,4},C={5,6} and D={5,6,7,8} Verify that
(i) A×(B∩C)=(A×B)∩(A×C)
(ii) A×C is a subset of B×D
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(i) To verify : A×(B∩C)=(A×B)∩(A×C)
We have B∩C={1,2,3,4}∩{5,6}=ϕ
∴ L.H.S = A×(B∩C)=A×ϕ=ϕ
A×B={(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4)}
A×C={(1,5),(1,6),(2,5),(2,6)}
∴R.H.S.=(A×B)∩(A×C)=ϕ
∴L.H.S=R.H.S
Hence A×(B∩C)=(A×B)∩(A×C)
(ii) To verify: A×C is a subset of B×D
A×C={(1,5),(1,6),(2,5),(2,6)}
B×D={(1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),
(3,8),(4,5),(4,6),(4,7),(4,8)}
We can observe that all the elements of set A×C are the elements of set B×D
Therefore A×C is a subset of B×D
Answer:
it is equal to 1 because 5/3 cancel by 3/5 3 cancel by 3 and 5 cancel by 5