State whether the set is finite or infinite: A={x:x∈N and (x−1)(x−2)=0}A = \{ x : x \in \mathbb{N} \text{ and } (x-1)(x-2) = 0 \}A={x:x∈N and (x−1)(x−2)=0}.
Solve the equation: (x−1)(x−2)=0 ⟹ x=1(x-1)(x-2) = 0 \implies x=1(x−1)(x−2)=0⟹x=1 or x=2x=2x=2. Both are natural numbers. A={1,2}A = \{1, 2\}A={1,2}. Since n(A)=2n(A) = 2n(A)=2, it is a Finite set.
Are sets A={x:x is a letter in ALLOY}A = \{x : x \text{ is a letter in ALLOY}\}A={x:x is a letter in ALLOY} and B={x:x is a letter in LOYAL}B = \{x : x \text{ is a letter in LOYAL}\}B={x:x is a letter in LOYAL} equal?
Perform operations on sets including Union, Intersection, and Power Sets.