Question

Two coins tossed simultaneously, consider the following events:
$A:$ Heads on both coins
$B:$ At least one head
Which of the following is/are true?

• A. $A\cup B=B$
• B. $A\cup B=A$
• C. $A\cap B=A$
• D. $A\cap B=B$

Answer 1

Answer: (A), (C)

$A\cap B=A$

$S=\{HH,HT,TH,TT\}$
$A=\left\{HH\right\},B=\{HT,TH,HH\}$
$A\cup B=\{HT,TH,HH\}=B$
$A\cap B=\left\{HH\right\}=A$