Question

Verify :

A= {-3,-2,-1,0,1,2},B={1,2,3,4},C={-2,-1,0,1}

i) Commutative property of union
ii) Distributive property of union over intersection

Please tell the answers with LHS and RHS and the answers must be completely solved ​

Answer 1

Answer:

Union is the smallest set which contains all the element of both the sets..

(i)commutative property of union is:-

A ∪ B = B∪A   or A∩B = B∩A

so,

A={-3,-2,-1,0,1,2}

B = {1,2,3,4}

so, LHS

A∪B = {-3,-2,-1,0,1,2,3,4} and

RHS,

B∪A = {-3,-2,-1,0,1,2,3,4}

Therefor, LHS = RHS Proved!

(ii) Distributive property:

A∪(B∩C) = (A∪B)∩(A∪C)

LHS, A∪(B∩C)

B∩C ={1}

now, A∪(B∩C) = {-3,-2,-1,0,1,2}

RHS , (A∪B)∩(A∪C)

A∪B = {-3,-2,-1,0,1,2,3,4}

A∪C ={-3,-2,-1,0,1,2}

(A∪B)∩(A∪C)= {-3,-2,-1,0,1,2}

therefor,

LHS = RHS poved!