Question

7. A = {5, 7, 9, 11, 13, 15) and B = {7, 8, 11, 15, 20) and C = {5, 8, 9, 11, 13, 15, 17, 20}
Verify that: A n (B n C) = (A n B) n C.

IF YOU CAN'T UNDERSTAND THE WRITTEN QUESTION PLEASE SEE PHOTO ONE.

PLEASE ANSWER CORRECT IF YOU DON'T KNOW THEN DO NOTHING.

THANK YOU.
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Answer 1

A = {5, 7, 9, 11, 13, 15 }

B = {7, 8, 11, 15, 20 }

C = {5, 8, 9, 11, 13, 15, 17, 20}

Now,

B ⋂ C = {8, 11, 15, 20} ...(1)

A ⋂ B = {7, 11, 15} ...(2)

Now,

==> A ⋂ ( B ⋂ C )

==> {5, 7, 9, 11, 13, 15} ⋂ {8, 11, 15, 20}

{ from (1) , B ⋂ C = {8, 11, 15, 20 }

==> A ⋂ (B ⋂ C) = {11, 15} ...(3)

Also,

==> (A ⋂ B) ⋂ C

==> {7, 11, 15} ⋂ {5, 8, 9, 11, 13, 15, 17, 20}

{ from (2), (A ⋂ B) = {7, 11, 15}

==> (A ⋂ B) ⋂ C = {11, 15} ...(4)

From (3) and (4)

==> A ⋂ (B ⋂ C) = (A ⋂ B) ⋂ C

Answer 2

✰✰|| Given ||✰✰

• Elements of A = 5,7,9,11,13,15

• Elements of B = 7,8,11,15,20

• Elements of C = 5,8,9,11,13,15,17,20

✰✰|| To Find ||✰✰

• prove A ∩ (B ∩ C) = (A ∩ B) ∩ C

✪|| Solution ||✪

A ∩ ( B ∩ C)

→ 5,7,9,11,13,15 ∩ ( 7,8,11,15,20 ∩ 5,8,9,11,13,15,17,20)

→ 5,7,9,11,13,15 ∩ 8,11,15

→ 11,15

(A ∩ B) ∩ C

→ ( 5,7,9,11,13,15 ∩ 7,8,11,15,20) ∩ 5,8,9,11,13,15,17,20

→ 11,15 ∩ 5,8,9,11,13,15,17,20

→ 11,15

A ∩ (B ∩ C) = (A ∩ B) ∩ C

→ 11,15 = 11,15

Hence, its proved that A ∩ (B ∩ C) = (A ∩ B) ∩ C