Question

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Answer 1

Given :-

• [A = {1, 3, 5, 7}]
• [B = {2, 6, 8}]
• [C = {3, 5, 6}]

To Find :-

• (a) (A ∪ B) ∩ C = ?
• (b) A ∩ (B U C) = ?

Solution :-

To calculate the this problem at first we have to know some rule. As we know ∩ is the sign of intersection and U is the sign of union section. To find the union section we have to keep the all members in the group which is present in two groups. ∩ we have to find the common members of two groups or more.

Calculation for (A ∪ B) ∩ C :-

⇒ [ (1, 3, 5, 7) ∪ (2, 6, 8) ] ∩ (3, 5, 6)

⇒ (1, 2, 3, 5, 6, 7, 8) ∩ (3, 5, 6)

⇒ (3, 5, 6)

Therefore , (A ∪ B) ∩ C = {3, 5, 6}

Calculation for A ∩ (B U C) :-

⇒ (1, 3, 5, 7) ∩ [ (2, 6, 8) U (3, 5, 6) ]

⇒ (1, 3, 5, 7) ∩ (2, 3, 5, 6, 8)

⇒ (3, 5)

Therefore A ∩ (B U C) = {3, 5}

Answer 2

Answer:

Question :-

• If A = {1, 3, 5, 7}; B = {2, 6, 8}; C = {3, 5, 6}. Find (a) (A $\sf \cup$ B) $\sf \cap$ C and (b) A $\sf \cap$ (B $\sf \cup$ C).

Given :-

• ☯ A = {1, 3, 5, 7}
• ☯ B = {2, 6, 8}
• ☯ C = {3, 5, 6}

To Find :-

• ☯ (a) (A $\sf \cup$ B) $\sf \cap$ C
• ☯ (b) A $\sf \cap$ (B $\sf \cup$ C)

Solution :-

☣ (A ∪ B) ∩ C :-

➙ [ (1, 3, 5, 7) $\sf \cup$ (2, 6, 8) ] $\sf \cap$ (3, 5, 6)

➙ (1, 2, 3, 5, 6, 7, 8) $\sf \cap$ (3, 5, 6)

➙ {3, 5, 6}

Henceforth, (A ∪ B) ∩ C = {3, 5, 6}

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☣ A ∩ (B U C) :-

➙ (1, 3, 5, 7) $\sf \cap$ [ (2, 6, 8) $\sf \cup$ (3, 5, 6) ]

➙ (1, 3, 5, 7) $\sf \cap$ (2, 3, 5, 6, 8)

➙ {3, 5}

Henceforth, A ∩ (B U C) = {3, 5}

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$\qquad\qquad\underline{\textsf{\textbf{ \color{magenta}{Extra\: Brainly\: Shots :-} }}}$

Union :

➳ The union of a set A with a B is the set of elements that are in either set A or B.

➳ The union is denoted as A $\bf \cup$ B.

Intersection :

✈ The intersection of a set A with a B is the set of elements that are in both set A and B.

✈ The intersection is denoted as A $\bf \cap$ B.