False. The statement does not logically follow from the given information.

[Magnetons]

Homework Statement

""If $4^2=16$, then $-1^2=1.$"" Is it true or false

Relevant Equations

No equation

I think it is "True" because the hypothesis is true and the conclusion is False.
But in the answer sheet, the answer is " This is False. The hypothesis is true, but the conclusion is false:$-1^2=-1$ , not1."

 

[FactChecker]

You are wrong and they are right. The fact that $4^2 = 16$ does not imply that $-(1^2)=1$. A true statement does not imply a false statement.

 

[sysprog]

Exponentiation precedes substraction (but follows parentheses) so $-1^2=-(1^2);~-1^2\neq(-1)^2$. Material implication, e.g. 'if $p$ then $q$' (symbolized $p\Rightarrow q$) is false if and only if the antecedent (in this instance $p$) is true and the consequent (in this instance $q$) is false.

 

[PeroK]

Homework Statement:: ""If $4^2=16$, then $-1^2=1.$"" Is it true or false

If $4^2 = 16$, then you owe me $1 million. True or false?

 

[PeroK]

... but, "If $4^2 =15$, then you owe me $1 million" is true, then you are safe enough.

 

[Steve4Physics]

Homework Statement:: ""If $4^2=16$, then $-1^2=1.$"" Is it true or false
Relevant Equations:: No equation

I think it is "True" because the hypothesis is true and the conclusion is False.
But in the answer sheet, the answer is " This is False. The hypothesis is true, but the conclusion is false:$-1^2=-1$ , not1."

‘Implies’ is a bit counter-intuitive. Just use the truth-table.

p	q	p→q
T	T	T
T	F	F
F	T	T
F	F	T

Note that p→q is true except when p is true and q is false.

 

[Magnetons]

You are wrong and they are right. The fact that $4^2 = 16$ does not imply that $-(1^2)=1$. A true statement does not imply a false statement.

I can only smile

If $4^2 = 16$, then you owe me $1 million. True or false?