Question

fill in the blank so that the resulting statement is true. set a is a subset of set b, expressed as ____, means that ____ choose the correct answer below. a. set a is a subset of set b, expressed as a⊆b, means that every element in set a is also an element in set b and sets a and b are not equal (a ≠ b) b. set a is a subset of set b, expressed as a⊆b, means that every element in set a is also an element in set b c. set a is a subset of set b, expressed as a⊂b, means that every element in set a is also an element in set b and sets a and b are not equal (a ≠ b) d. set a is a subset of set b, expressed as a⊂b, means that every element in set a is also an element in set b

Explanation:

To determine the correct answer, we recall the definition of a subset. A subset \( A \subseteq B \) means every element of \( A \) is also an element of \( B \). A proper subset (\( A \subset B \)) requires \( A \subseteq B \) and \( A
eq B \).

• Option A: Incorrect, as \( A \subseteq B \) does not require \( A

eq B \) (they can be equal, making \( A \) a subset, not necessarily proper).

• Option B: Correct, as \( A \subseteq B \) is defined as every element of \( A \) being in \( B \) (equality is allowed).
• Option C: Incorrect, as \( A \subset B \) (proper subset) requires \( A

eq B \), but the notation here is misused (the question uses \( \subseteq \) in the option’s description, conflicting with \( \subset \)).

• Option D: Incorrect, as \( A \subset B \) is a proper subset, but the question asks for "subset" (which includes equality), so the notation \( \subset \) is wrong here.

Answer:

B. Set A is a subset of set B, expressed as \( A\subseteq B \), means that every element in set A is also an element in set B