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If \( \Large A=\{ 1, 3, 5, 7 \},\ B=\{ 1, 2, 4, 6, 8 \},\ C=\{ 1, 3, 6, 8 \} \) then finr \( \Large A\cap \left(B\cup C\right) \) and \( \Large \left(A\cap B\right)\cup \left(A\cap C\right) \)

A) \( \Large \{ 1, 3 \} \)
B) \( \Large \{ 3, 5 \} \)
C) \( \Large \{ 6, 8 \} \)
D) None of these

Correct Answer:

A) \( \Large \{ 1, 3 \} \)

Description for Correct answer:
\( \Large A=\{ 1, 3, 5, 7 \},\ B=\{ 1, 2, 4, 6, 8 \},\ C=\{ 1, 3, 6, 8 \} \)

\( \Large A\cap B = \{ 1 \} \)

\( \Large A\cap C = \{ 1, 3 \} \)

\( \Large B\cap C = \{ 1, 6, 8 \} \)

\( \Large B\cup C = \{ 1, 2, 3, 4, 6, 8 \} \)

\( \Large A\cap \left(B\cup C\right) = \{ 1, 3 \} \)

\( \Large \left(A\cap B\right)\cup \left(A\cap C\right) = \{ 1 \}\{ 1, 3 \} \)

=\( \Large \{ 1, 3 \} \)

Part of solved Set theory questions and answers : >> Elementary Mathematics >> Set theory

Comments

Similar Questions

1). If \( \Large E=\{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \}; \) \( \Large A=\{ 1, 3, 5, 7 \},\ B=\{ 2, 4, 6, 8 \} \) then find the value of \( \Large \left(A\cup B\right)' \) and \( \Large A'\cap B' \)

A). \( \Large \{ 6 \} \)

B). \( \Large \{ 9 \} \)

C). \( \Large \{ \} \)

D). None of these

2). If \( \Large A=\{ 1, 2, 3, 4 \},\ B=\{ 3, 4, 5, 6 \},\ C=\{ 6, 7, 8, 9 \} \) then find the set \( \Large A\cap \left(B\cup C\right) \)

A). \( \Large \{ 1, 2 \} \)

B). \( \Large \{ 2, 3 \} \)

C). \( \Large \{ 3, 4 \} \)

D). \( \Large \{ 6, 7 \} \)

3). \( \Large A=\{ 1, 2, 3, 4 \},\ B=\{ 3, 4, 5, 6 \},\ C=\{ 6, 7, 8, 9 \} \) then find the set \( \Large A- \left(B\cup C\right)\ and\ \left(A-B\right)\cap \left(A-C\right) \)

A). \( \Large \{ 1, 2 \} \)

B). \( \Large \{ 3, 4 \} \)

C). \( \Large \{ 6, 7 \} \)

D). \( \Large \{ 8, 9 \} \)

4). \( \Large A=\{ 4, 9, 16, 25, 36 \},\ B=\{ 9, 25, 49, 81 \},\ C=\{ 16, 81, 256 \} \) then find \( \Large A- \left(B\cap C\right) \)

A). \( \Large \{ 81 \} \)

B). \( \Large \{ 4, 9, 16, 25, 36 \} \)

C). \( \Large \{ 4, 36 \} \)

D). \( \Large \{ 4, 16, 36 \} \)

5). If \( \Large n \left(A\right)=6, n \left(B\right)=5, n \left(A\cap B\right)=3 \) then find \( \Large n \left(A\cup B\right) \)

A). 11

B). 9

C). 8

D). None of these

6). lf \( \Large A=\{ 1, 2, 3, 4, 5, 6 \},\ B=\{ 4, 5, 6 \} \), then \( \Large n \left(A\cap B\right) \)

A). 3

B). 6

C). 4

D). 2

7). If \( \Large n \left(p \left(A\right)=16 \right) \) then what is the value of \( \Large n \left(A\right) \)

A). 12

B). 4

C). 8

D). 2

8). If \( \Large A=\{ 4, 5, 6, 7, 8, 9, 10 \},\ A\cap B=\{ 6, 7, 8 \},\ A\cup B=\{ 4, 5, 6, 7, 8, 9, 10, 11, 12 \} \), then find B.

A). \( \Large \{ 4, 5, 6, 7, 8 \} \)

B). \( \Large \{ 6, 7, 8, 11, 12 \} \)

C). \( \Large \{ 4, 5, 7, 10, 11, 12 \} \)

D). None of these

9). If \( \Large E=\{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \},\ A=\{1, 2, 3, 4, 5 \},\ B=\{2, 4, 6, \} \) then find \( \Large \left(A\cup B\right)' \)

A). \( \Large \{ 8, 9 10 \} \)

B). \( \Large \{ 7, 8, 9 10 \} \)

C). \( \Large \{ 6, 7, 8, 9, 10 \} \)

D). cannot be found

10). \( \Large n \left(A\cup B\right)=8,\ n \left(A\right)=6,\ n \left(B\right)=4 \) find \( \Large n \left(A\cap B\right) \)

A). 10

B). 7

C). 2

D). 4