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  • Show that the statement p: “If x is a real number such that x^3 + 4x = 0, then x is 0” is true by (i) direct method,

1.(i)    Show that the statement
           p: “If x is a real number such that x^3 + 4x = 0, then x is 0” is true by
           (i) direct method,

Answers (1)

best_answer

If x is a real number such that x^3 + 4x = 0, then x is 0 : (if p then q)

p: x is a real number such that x^3 + 4x = 0.

q: x is 0.

In order to prove the statement “if p then q” 

Direct Method:  By assuming that p is true, prove that q must be true.

So,

p is true:There exists a real number x such that x^3 + 4x = 0 \implies x(x^2 + 4) = 0

\implies x = 0\ or\ (x^2 + 4)= 0

\implies x = 0\ or\ x^2 = -4\ (not\ possible)

Hence, x = 0

Therefore q is true.

Posted by

HARSH KANKARIA

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