生成一个视频。包含所有的题目的讲解---Here is the extracted content from the image:
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**Question 41:**
**Question Stem:** 已知集合 M={x|x²-2x-3≤0}, N={x|y=lg (x-2)}, 则 M∪N = ( )
(Translation: Given set M={x|x²-2x-3≤0}, N={x|y=lg (x-2)}, then M∪N = ( ))
**Options:**
A. [-1, +∞)
B. (-1, +∞)
C. (2, 3]
D. (1, 3]
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**Question 42:**
**Question Stem:** 集合 M={y|y=ln (x²+1)}, N={x|2ˣ<4}, 则 M∩N 等于 ( )
(Translation: Given set M={y|y=ln (x²+1)}, N={x|2ˣ<4}, then M∩N equals ( ))
**Options:**
A. [0, 2]
B. (0, 2)
C. [0, 2)
D. (0, 2]
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**Question 43:**
**Question Stem:** 设集合 A={-1, 0, 1, 2}, B={x||x|=k-|y|, x∈A, y∈A}, 则集合 A∩B = ( )
(Translation: Let set A={-1, 0, 1, 2}, B={x||x|=k-|y|, x∈A, y∈A}, then set A∩B = ( ))
**Options:**
A. {0, 1}
B. {0, 1, 2}
C. {0, 1, 2, 3}
D. {-1, 0, 1, 2}
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**Question 44:**
**Question Stem:** 设集合 A={-2, -1, 0, 1, 2}, B={-1, 0, 1}, C={(x, y)| (x²/4) + (y²/3) ≤1, x∈A, y∈B}, 则集合 C 中元素的个数为 ( )
(Translation: Let set A={-2, -1, 0, 1, 2}, B={-1, 0, 1}, C={(x, y)| (x²/4) + (y²/3) ≤1, x∈A, y∈B}, then the number of elements in set C is ( ))
**Options:**
A. 11
B. 9
C. 6
D. 4
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**Question 45:**
**Question Stem:** 设集合 M={x||x|<1}, N={y|y=2ˣ, x∈M}, 则集合 M∩N = ( )
(Translation: Let set M={x||x|<1}, N={y|y=2ˣ, x∈M}, then set M∩N = ( ))
**Options:**
A. (-∞, 1/2]∪[1, +∞)
B. (1/2, 1)
C. (-∞, 1/2]
D. [1, +∞)
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**Question 46:**
**Question Stem:** 已知集合 A={(x, y)|y=2x}, B={(x, y)|y=(x²-1)/(x+1)}, 则 A∩B 为 ( )
(Translation: Given set A={(x, y)|y=2x}, B={(x, y)|y=(x²-1)/(x+1)}, then A∩B is ( ))
**Options:**
A. ∅
B. {-1, -2}
C. {(1, 2)}
D. {(-1, -2)}
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**Question 47:**
**Question Stem:** 设集合 A={x|x²-4x+3<0}, B={x||x|²-8>0}, 则 A∩B = ( )
(Translation: Let set A={x|x²-4x+3<0}, B={x||x|²-8>0}, then A∩B = ( ))
**Options:**
A. (-3, -3/2)
B. (-3, 3/2)
C. (1, 3/2)
D. (3/2, 3)
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**Question 48:**
**Question Stem:** 已知集合 A={x|y=√(2-x²), x∈R}, B={x|-1≤x≤3, x∈Z}, 则集合 A∩B 中元素的个数为 ( )
(Translation: Given set A={x|y=√(2-x²), x∈R}, B={x|-1≤x≤3, x∈Z}, then the number of elements in set A∩B is ( ))
**Options:**
A. 4
B. 3
C. 2
D. 1