Question

P is the solution set of - 3x + 4 < 2x - 3, xe N, and Q is the solutio
4-5 < 12, xe W, find P unit Q and Q-P plz help me

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Answer 1

SOLUTION

GIVEN

P is the solution set of -3x + 4 < 2x - 3, x ∈ N, and is the solution set of 4x - 5 < 12, x ∈ W.

TO DETERMINE

(i) P ∩ Q (ii) Q - P

EVALUATION

SOLVE FOR FIRST INEQUALITY

$\displaystyle\sf{ - 3x + 4 < 2x - 3}$

$\displaystyle\sf{ \implies \: - 5x < - 7}$

$\displaystyle\sf{ \implies \: 5x > 7}$

$\displaystyle\sf{ \implies \: x > 1.4}$

So the solution set

P = { 2 , 3 , 4 , 5 ,...}

SOLVE FOR SECOND INEQUALITY

$\displaystyle\sf{ 4x - 5< 12}$

$\displaystyle\sf{ \implies \: 4x< 17}$

$\displaystyle\sf{ \implies \: x< 4.25}$

So the solution set

Q = { 0 , 1 , 2 , 3 , 4 }

∴ P ∩ Q = { 2 , 3 , 4 }

Also

P - Q = { 5 , 6 , 7 ,..}

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