let A and B be subsets of some universal set U Are the follo

let A and B be subsets of some universal set U. Are the following propositions true or false? Justify the conclusions.

Solution

(a)

False,

Let,C={1,2,3}

A={1,2,4,5,6,7}

B={1,2,3}

A intersection C={1,2}

B intersection C={1,2,3}

But A is not subset of B

b)

False

A={1,2,3},C={3,4,5}, B={1,2}

A union C={1,2,3,4,5},B union C={1,2,3,4,5}

But A is not subset B

c)

False

A={1,2,3},C={3,4,5}, B={1,2}

A union C={1,2,3,4,5},B union C={1,2,3,4,5}

A union C = B union C

But A is not equal to B

e)

True

Let x be in A not C. So x is in A union C and hence in B union C. But x is not in C so x is in B

Let x be in A and C ie A intersection C so x is in B intersection C.

But, A=(A-C)union A intersection C

A-C=B-C

A intersection C =B intersection C

Hence, A=B