Question

IF A={P, Q, R, S}, B={M, N, Q, S, T} AND C={M, N, P, Q, S}, THEN VERIFY THE ASSOCIATIVE PROPERTY OF UNION OF SETS

Answer 1

GIVEN :

If $A={\{p, q,r, s}\}$, $B={\{m,n,q,s,t}\}$ and $C={\{m,n,p,q,s} \}$ then verify the Associative property of Union of the given sets.

TO VERIFY :

The Associative property of Union of sets.

SOLUTION :

Given that the sets are  A={p, q,r, s}, B={m,n,q,s,t} and C={m,n,p,q,s}

For any sets A ,B and C the Associative property of Union of sets is given by :

$A\cup (B\cup C)=(A\cup B)\cup C$

Now we have to find the LHS $A\cup (B\cup C)$

$(B\cup C)={\{m,n,q,s,t}\}\cup {\{m,n,p,q,s}\}$

$B\cup C={\{m,n,p,q,s,t}\}$

$A\cup (B\cup C)={\{p, q,r, s}\}\cup {\{m,n,p,q,s,t}\}$

$A\cup (B\cup C)={\{m,n,p,q,r,s,t}\}\hfill (1)$=LHS

Now taking the RHS $(A\cup B)\cup C$

$(A\cup B)={\{p, q,r, s}\}\cup {\{m,n,q,s,t}\}$

$(A\cup B)={\{m,n,p,q,r,s,t}\}$

$(A\cup B)\cup C={\{m,n,p,q,r,s,t}\}\cup {\{m,n,p,q,s}\}$

$(A\cup B)\cup C={\{m,n,p,q,r,s,t}\}\hfill (2)$=RHS

From the equations (1) and (2) we get LHS=RHS

∴ $A\cup (B\cup C)=(A\cup B)\cup C$

∴ The Associative property of Union for the given sets is verified.

Answer 2

Answer:

associative property of Union of sets