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Mathematics

Find which of the following sets are singleton sets :

(i) The set of points of intersection of two non-parallel straight lines on the same plane.

(ii) A = {x : 7x - 3 = 11}

(iii) B = {y : 2y + 1 < 3 and y ∈ W}

Sets

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Answer

(i) There will be always one and only point where two non-parallel straight lines meet on the same plane.

Hence, this is a singleton set.

(ii) 7x - 3 = 11

7x = 11 + 3

7x = 14

x = 147\dfrac{14}{7}

x = 2

A = {2}. Hence, A is a singleton set.

(iii) 2y + 1 < 3

2y < 3 - 1

2y < 2

y < 22\dfrac{2}{2}

y < 1

B = {0}. Hence, B is a singleton set.

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