Question

Let A = {x∈Z: -1 ≤ x < 4} and let B = {x ∈ Z:0 < \(\frac{x}{2}\) ≤ 3}. Then A∩B is equal to

• A. {1,2,3}
• B. {2,3}
• C. {1,2,3,4}
• D. {2,3,4}
• E. {0,1,2,3}

Answer 1

The Correct Option is A

The set \( A \) is defined as \( A = \{ x \in \mathbb{Z} : -1 \leq x < 4 \} \), which translates to \( A = \{-1, 0, 1, 2, 3\} \).  
The set \( B \) is defined as \( B = \{ x \in \mathbb{Z} : 0 < \frac{x}{2} \leq 3 \} \), which simplifies to \( B = \{1, 2, 3, 4, 5, 6\} \).  
The intersection of sets \( A \) and \( B \), denoted \( A \cap B \), includes the elements that are common to both sets. 

The correct option is (A) : \( \{1, 2, 3\} \)

Answer 2

We are given two sets:

• A = {x ∈ Z: -1 ≤ x < 4}
• B = {x ∈ Z: 0 < \(\frac{x}{2}\) ≤ 3}

Let's determine the elements of each set:

• A consists of integers x such that -1 ≤ x < 4. So A = {-1, 0, 1, 2, 3}.
• B consists of integers x such that 0 < \(\frac{x}{2}\) ≤ 3. Multiplying by 2, we get 0 < x ≤ 6. So B = {1, 2, 3, 4, 5, 6}.

Now, we need to find the intersection of A and B (A ∩ B), which contains the elements that are common to both sets:

A ∩ B = {-1, 0, 1, 2, 3} ∩ {1, 2, 3, 4, 5, 6} = {1, 2, 3}

Therefore, A ∩ B is equal to {1, 2, 3}.