Question

16. (5 points) Identify the truth value of the statement Vr (r2 +2> 1) where the domain is R. If it is true, explain why; if it is not, provide a counterexample. True, All real number ather whole or Are greater than 17 nhy Fractional 17. (5 points) Identify the truth value of the statement 3r (r2 = 2) where the domain is Z. If it is true, provide an example; if it is not, explain why This is Trme False VEnot anintger X O

Answer 1

Q16)Ans:-True,because

• when we square a positive number we get a positive result, like 2²=4
• when we square a negative number we also get a positive result (because a negative times a negative gives a positive), for example (-2)²= +4

Additional information:-

for all x,x²+2>1 will fall in FALSE, when x is complex number which is not real real number,because

when we square the complex number it will give negative number as result

ex:-    lets take a complex number as x=3i

           (3i)²+2=9(-1)+2 //in complex numbers i²=-1

          =>-7 which is less than 1

Q17)Ans:False,because

Z denotes all positive numbers and zero and negative numbers and does not denotes rational and irrational numbers.

Given x²=2 i.e x=2^1/2 which is irrational number and not an integer. And,irrational numbers are not part of Z.

so the given statement is False.