Question

In the event of tossing of two coins, let $A=\{HH,HT\}$ and $B=\{HT,TT\}$. Then which of the following is/are true $?$

• A. $(A\cap B)=\varphi$
• B. $(A\cap B)=\left\{HT\right\}$
• C. $(A\cup B)=\{HH,HT,TT\}$
• D. $(A\cup B)=\varphi$

Answer 1

Answer: (B), (C)

$(A\cup B)=\{HH,HT,TT\}$

$(A\cup B)\Rightarrow$ the collection of all the events of $A$ as well as $B$.
Hence $(A\cup B)=\{HH,HT,TT\}$
$(A\cap B)\Rightarrow$ the events which are common to both $A$ as well as $B$.
Hence $(A\cap B)=\left\{HT\right\}$