Question:
Let A = \(\{x : x \notin R, x \geq 4\}\) and B = \(\{x : x \notin R, x < 5\}\) then A ∩ B is
मान लीजिए \(A = \{x : x \notin R, x \geq 4\}\) और \(B = \{x : x \notin R, x < 5\}\) है, तो \(A \cap B\) क्या है?
Options:
- \(\{x : x \in R,\ 4 \leq x < 5\}\)
- \(\{4, 5\}\)
- \(\{4\}\)
- \(\{5, 4\}\)
- \(\{x : x \in R,\ 4 \leq x < 5\}\)
- \(\{4, 5\}\)
- \(\{4\}\)
- \(\{5, 4\}\)
Correct Answer: a)
Explanation:
Here, set \(A = \{x : x \in \mathbb{R}, x \geq 4\} = [4, \infty)\) and set \(B = \{x : x \in \mathbb{R}, x < 5\} = (-\infty, 5)\).
The intersection is \(A \cap B = [4, \infty) \cap (-\infty, 5) = [4, 5) = \{x : x \in \mathbb{R}, 4 \leq x < 5\}\).
यहाँ, समुच्चय \(A = \{x : x \in \mathbb{R}, x \geq 4\} = [4, \infty)\) और समुच्चय \(B = \{x : x \in \mathbb{R}, x < 5\} = (-\infty, 5)\) हैं।
इनका सर्वनिष्ठ \(A \cap B = [4, \infty) \cap (-\infty, 5) = [4, 5) = \{x : x \in \mathbb{R}, 4 \leq x < 5\}\) है।