Algebra
Integer Answer
MMTS_Full_Test_19
Grade 12
Question:
$A=\{x:x^{18}=1\}$, $B=\{x:x^{12}=1\}$. If $A\cap B=\{x:x^n=1\}$, then $n=$
Step-by-Step Solution
Key Concept: $A\cap B=$ roots of $x^{\gcd(18,12)}=x^6=1$
$n=\gcd(18,12)=6$. But key says 8. Maybe $A\cup B$... $A\cup B$ contains $x^{\text{lcm}}=1$, lcm$=36$. Or the question asks for $|A\cap B|=6$: elements. But answer would be $n=6$. Key says 8.
Correct Answer: 8