Fsc Part 1 Mathematics (Complete Solution)

Q1
verify the commutative properties of union and intersection for the following pairs of sets

(i) A={1,2,3,4,5}, B={4,6,8,10}

SOLUTION:

AUB={1,2,3,4,5}U{4,6,8,10}={1,2,3,4,5,6,8,10}=BUA

this satisfies the commutative property of union.

A∩B={1,2,3,4,5}∩{4,6,8,10}={4}=B∩A

this satisfies the commutative property of intersection.

(ii) N,Z

SOLUTION:

we have to prove that the property of union.

NUZ=ZUN

L.H.S=NUZ

     =Z

R.H.S=ZUN

       =Z

this satifies the commulative property of union.

Now we to prove that property of intersection.

N∩Z=N=Z∩A

this satisfies the commutative property of intersection.

(iii) A={x l x ∈ R ∧ x ≥ 0}, B=R

SOLUTION:

we have to prove commulative property of union.

AUB=BUA

L.H.S=AUB={x l x ∈ R ∧ x ≥ 0}UR=R

Now taking R.H.S,we have,

R.H.S=BUA=RU{x l x ∈ R ∧ x ≥ 0}=R

L.H.S=R.H.S

So this satisfies the commutative property of union.

We have to prove commutative property of intersection.

A∩B={x l x ∈ R ∧ x ≥ 0}∩R={x l x ∈ R ∧ x ≥ 0}=A=B∩A

this satisfies the commutative property of intersection.

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