Show that set B - y-2y-1-3 and y - W is a singleton set-

B= { y:2y+1 lt;3 and y ∈ W } 2y+1 lt;3 ⇒ 2y+1 1 lt;3 1 (Subtracting 1 from both sides) ⇒ 2y lt;2 ⇒ y lt;2/2 (Dividing both sides by 2) ⇒ ...

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Standard VI

Mathematics

Properties of a Set

Show that set...

Question

Show that set $B = {y : 2 y + 1 < 3 a n d y \in W}$ is a singleton set.

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Solution

$B = {y : 2 y + 1 < 3 a n d y \in W} 2 y + 1 < 3 \Rightarrow 2 y + 1 - 1 < 3 - 1 (Subtracting 1 from both sides) \Rightarrow 2 y < 2 \Rightarrow y < \frac{2}{2} (Dividing both sides by 2) \Rightarrow y < 1 ∴ B = {0} Hence set B is a singleton set.$

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Similar questions

Show that the solution set of the following linear inequations is empty set:

(i) $x - 2 y \geq 0, 2 x - y \leq - 2, x \geq 0, y \geq 0$

(ii) $x + 2 y \leq 3, 3 x + 4 y \geq 12, y \geq 1, x \geq 0 a n d y \geq 0$

State which of the following sets are singleton sets.
$(i) A = {x | x = 16}$
$(i i) B = {y | y^{2} = 36}$
$(i i i) C = {p | p \in I, p^{3} = - 8}$
$(i v) D = {q | (q - 4)^{2} = 0}$
$(v) E = {x | 1 + 2 x = 3 x, x \in W}$

Q. Show that set

B = {y : 2 y + 1 < 3 a n d y \in W}

is a singleton set.

Q. Set

B = {y : 2 y + 1 < 3 a n d y \in W}

is a/an ___ .

Q. Find the following set is singleton set or not.

B = {

y

2 y + 1 < 3

and

Y ϵ W

}

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Show that set B={y:2y+1<3 and y∈W} is a singleton set.

B={y:2y+1<3 and y ∈ W}2y+1<3⇒ 2y+1−1<3−1 (Subtracting 1 from both sides)⇒ 2y<2⇒ y<22 (Dividing both sides by 2)⇒ y<1∴ B={0}Hence set B is a singleton set.

Show that set $B = {y : 2 y + 1 < 3 a n d y \in W}$ is a singleton set.

$B = {y : 2 y + 1 < 3 a n d y \in W} 2 y + 1 < 3 \Rightarrow 2 y + 1 - 1 < 3 - 1 (Subtracting 1 from both sides) \Rightarrow 2 y < 2 \Rightarrow y < \frac{2}{2} (Dividing both sides by 2) \Rightarrow y < 1 ∴ B = {0} Hence set B is a singleton set.$