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

             (iii) method of contrapositive

Answers (1)

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” 

Contrapositive Method:  By assuming that q is false, prove that p must be false.

So,

q is false: x \neq 0

\implies x.(Positive number) \neq 0.(Positive number)

\implies x(x^2 + 4) \neq 0(x^2 + 4)

\implies x(x^2 + 4) \neq 0 \implies x^3 + 4x \neq 0

Therefore p is false.

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