If A,B and C are three sets such that `A cap B = A cap C and A cup B = A cup C ` then

If A,B and C are three sets such that `A cap B = A cap C and A cup B = A cup C ` then
A. A=B
B. A=C
C. B=C
D. `A cap B = phi `

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

Salim Ahmed Kawsar

Correct Answer - C
`B=B cap (A cup B)`
`=B cap (A cup C)" " (therefore A cup B= A cup C)`
`=(B cap A)cup (B cap C ) `
`= (B cap A)cup (B cap C) `
`= ( A cap B )cup (B cap C) `
`(A cap C) cup (B cap C) " " (therefore A cap B = A cap C)`
`=(A cup C) cap C`
`(A cup C)cap C`
=C

4 views Answered 2023-02-05 15:29

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