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Write down the truth set of each of the ...

Write down the truth set of each of the following open sentences :
(i) `p(x): x+5lt9,x in N.`
(ii) `p(x): x+3 lt 3, x in N.`
(iii) `p(x): x+5gt7, x in R.`
(iv) `p(x): 2x^(2)+5x-3=0, x in I,`

Text Solution

Verified by Experts

We have:
(i) Truth Set= `{x in N: x+5 lt 9}`
`={x in N: x lt4}={1,2,3}`
(ii) Truth Set `={x in N: x+3 lt 3}`
`={x in N: x lt 0}=phi`
(iii) Truth Set `={x in R: x+5gt7}`
`={x in R: x gt2}=]2, oo[.`
(iv) `2x^(2)+5x-3=0rArr2x^(2)+6x-x-3=0rArr2x(x+3)-(x+3)=0 rArr (x+3)(2x-1)=0rArrx=-3or x=(1)/(2).`
`therefore" truth set "={x in I:2x^(2)+5x-3=0}={-3}" "[because (1)/(2) in I]`
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