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Question

Write down the truth set of each of the following open sentences:

(i) p(x):x+5<9,xN.

(ii) p(x):x+3<3,xN.

(iii) p(x):x+5>7,xR.

(iv) P(x):2x2+5x3=0, x1

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Solution

We have:

(i) Truth Set = {xN:x+5<9}

{xN:x<4}={1,2,3}

(ii) Truth Set = {xN:x+3<3}

{xN:x<0}=Φ.

(iii) Truth Set = {xR:x+5>7}

{xR:x>2}=]2, [

(iv) 2x2+5x3=02x2+6xx3=02x(x+3)(x+3)=0

(x+3)(2x1)=0x=3 or x=12.

truth set = {xl:2x2+5x3=0}={3}[12l]


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