Consider the following statements:
P: Every compact metrizable topological space is separable.
Q: Every Hausdorff topology on a finite set is metrizable.
Then,
P: Every compact metrizable topological space is separable.
Q: Every Hausdorff topology on a finite set is metrizable.
Then,
Show Hint
- both P and Q are TRUE
- P is TRUE and Q is FALSE
- P is FALSE and Q is TRUE
- both P and Q are FALSE
The Correct Option is A
Solution and Explanation
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Consider the following regions: \[ S_1 = \{(x_1, x_2) \in \mathbb{R}^2 : 2x_1 + x_2 \leq 4, \quad x_1 + 2x_2 \leq 5, \quad x_1, x_2 \geq 0\} \] \[ S_2 = \{(x_1, x_2) \in \mathbb{R}^2 : 2x_1 - x_2 \leq 5, \quad x_1 + 2x_2 \leq 5, \quad x_1, x_2 \geq 0\} \] Then, which of the following is/are TRUE?
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The following statements are made based on the relationships given above.
(1) R is the grandmother of S.
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For \( X = (x_1, x_2, x_3)^T \in \mathbb{R}^3 \), consider the quadratic form:
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