Solve this question from Linear Inequations chapter ICSE syllabus.
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If P is the solution set of -3x+4< 2x-3, x∈N, and Q is the solution set of 4x-5<12, x∈W, find (i) P∩Q (ii) Q-P.
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−3x+4<2x−3
⇒−3x−2x<−3−4
⇒−5x<−7
⇒x>
5
7
As x∈N
The solution set P is {2,3,4,5,…}
And
4x−5<12
⇒4x<12+5
⇒4x<17
⇒x<
4
17
As x∈W
The solution set Q is {0,1,2,3,4}
Therefore,
(i) P∩Q={2,3,4}
(ii) Q−P={0,1}
i ) {2,3,4}
ii). {1,0}