ISRO CSE 2020 | Question: 76

Question

If $A=\{x,y,z\}$ and $B=\{u,v,w,x\}, $ and the universe is $\{s,t,u,v,w,x,y,z\}$. Then $(A \cup \overline{B}) \cap (A \cap B)$ is equal to

• A. $\{u,v,w,x\}$
• B. $\{ \: \}$
• C. $\{u,v,w,x,y,z\}$
• D. $\{u,v,w\}$

Comments

i have not marked any option

so marks will be given to all or only who have attempted?

---

The question would be canceled.

Answer 1

$\bar{B}=\{s,t,u,v,w,x,y,z\}-\{u,v,w,x\} = \{s,t,y,z\}$

$(A\cup\bar{B})=\{s,t,x,y,z\}$

$(A\cap B)=\{x\}$

$(A\cup \bar{B})\cap(A\cap B)=\{s,t,x,y,z\}\cap\{x\}=\{x\}$

But there was no such option.

Comments

A={x,y,z}

B={u,v,w,z}

U={s,t,u,v,w,x,y,z}

B¯ = U-B

     = {s,t,u,v,w,x,y,z}-{u,v,w,z} => {s,t,x,y}

A U B¯  = { s,t,x,y,z}

A ∩  B = { x,y,z} ∩ {u,v,w,z } => { z }

(A U B¯)  ∩ (A ∩  B) = { s,t,x,y,z} ∩ { z } => {z}

Ans is {z}

not {x}

---

set $B$  having element $(u,v,w,x)$ but you taken as $(u,v,w,z)$