The number of elements in the set S = {x in m | vedclass

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(C) Given $S = \{x \in \mathbb{Z} : x^2 - 7x + 6 \leq 0 	ext{ and } x^2 - 3x > 0\}$ ...$(i)$First,solve the inequality $x^2 - 7x + 6 \leq 0$:$(x - 6)

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$3$

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(C) Given $S = \{x \in \mathbb{Z} : x^2 - 7x + 6 \leq 0 	ext{ and } x^2 - 3x > 0\}$ ...$(i)$First,solve the inequality $x^2 - 7x + 6 \leq 0$:$(x - 6)(x - 1) \leq 0$This implies $x \in [1, 6]$.Next,solve the inequality $x^2 - 3x > 0$:$x(x - 3) > 0$This implies $x \in (-\infty, 0) \cup (3, \infty)$.Now,find the intersection of these two intervals:$S = \{x \in \mathbb{Z} : x \in [1, 6] \cap ((-\infty, 0) \cup (3, \infty))\}$$S = \{x \in \mathbb{Z} : x \in (3, 6] \cap \mathbb{Z}\}$$S = \{4, 5, 6\}$.The number of elements in set $S$ is $3$.

The number of elements in the set $S = \{x \in \mathbb{Z} : x^2 - 7x + 6 \leq 0 \text{ and } x^2 - 3x > 0\}$ is

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