Question

3. The following sets are not equal - An (BUC) and AU(BnC) Construct a universe U and non-empty sets A, B, and C so that the above sets are in fact the same. . Construct a universe U and non-empty sets A, B, and C so that the above sets are in fact different.

Answer 1

Answer:

1.U={1,2,3,4,5}

A={2}

B={2,3}

C={4,5}

2.U={1,2,3,4}

A={1,2}

B={2,3}

C={4}

Step-by-step explanation:

We are given that $A\cap (B\cup C)$ and $A\cup (B\cap C)$

are different sets

1.We have to construct a universe set U and non empty sets A,B and C so that above set in fact the same

Suppose U={1,2,3,4,5}

A={2}

B={2,3}

C={4,5}

$B\cap C=\phi$

$B\cup C=${2,3,4,5}

$A\cap (B\cup C)$={2}$\cap${2,3,4,5}={2}

$A\cup (B\cap C)$={2}$\cup\phi$={2}

Hence, $A\cap (B\cup C)=A\cup (B\cap C)$

2.We have to construct a universe set U and non empty sets A,B and C so that  above sets are in fact different

Suppose U={1,2,3,4}

A={1,2}

B={2,3}

C={4}

$B\cap C=\phi$

$B\cup C$={2,3,4}

$A\cup (B\cap C)$={1,2}$\cup \phi$={1,2}

$A\cap (B\cup C)$={1,2}$\cap$ {2,3,4}={2}

Hence, $A\cap (B\cup C)\neq A\cup (B\cap C)$