Question

16. If A={p,q,r,s), B={m, n,q,s,t}, C={m,n,p,q,s} verify associative property of union of sets.​

Answer 1

GIVEN:

• A = {p, q, r, s}

• B = {m, n, q, s, t}

• C = {m, n, p, q, s}

TO VERIFY:

• The associative property of union of sets.

PROPERTY:

$\boxed{ \gray{ \boldsymbol{ \large{A \cup(B\cup C)=(A \cup B) \cup C}}}}$

VERIFICATION:

$\sf L.H.S: A \cup(B\cup C)$

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

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

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

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

$\sf R.H.S:(A \cup B) \cup C$

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

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

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

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

$\sf L.H.S = R.H.S = \{m, n,p, q, r, s, t \}$

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

HENCE VERIFIED.

Answer 2

Answer:

✡ Question ✡

☞ If A={p,q,r,s), B={m, n,q,s,t}, C={m,n,p,q,s} verify associative property of union of sets.

✡ Given ✡

☞ A = {p, q, r, s}

☞ B = {m, n, q, s, t}

☞ C = {m, n, p, q, s}

✡ To Verify ✡

☞ The associative property of union of sets.

✡ Verification ✡

$\huge \bold{ \underline{ \mathbb{ \blue{</em></strong><strong><em>L</em></strong><strong><em>.</em></strong><strong><em>H</em></strong><strong><em>.</em></strong><strong><em>S</em></strong><strong><em>}}}}$

▶A∪(B∪C)

=> B∪C={m,n,q,s,t}∪{m,n,p,q,s}

=> B∪C={m,n,p,q,s,t}

=> A∪(B∪C)={p,q,r,s}∪{m,n,p,q,s,t}

=> A∪(B∪C)={m,n,p,q,r,s,t}

$\huge \bold{ \underline{ \mathbb{ \blue{</em></strong><strong><em>R.H</em></strong><strong><em>.</em></strong><strong><em>S</em></strong><strong><em>}}}}$

▶(A∪B)∪C

=> A∪B={p,q,r,s}∪{m,n,q,s,t}

=> A∪B={m,n,p,q,r,s,t}

=> (A∪B)∪C={m,n,p,q,r,s,t}∪{m,n,p,q,s}

=> (A∪B)∪C={m,n,p,q,r,s,t}

L.H.S=R.H.S={m,n,p,q,r,s,t}

A∪(B∪C)=(A∪B)∪C

HENCE VERIFIED.

Step-by-step explanation:

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