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

In summary: If ##4^2 =15##, then you owe me $1 million" is true, then you are safe enough.In summary, the conversation discusses the concept of material implication and its truth table. It is stated that if the hypothesis is true and the conclusion is false, then the statement is false. The conversation also presents an example to illustrate this concept.
  • #1
Magnetons
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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.
:cry::cry:But in the answer sheet, the answer is " This is False. The hypothesis is true, but the conclusion is false:## -1^2=-1## , not1."
 
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  • #2
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.
 
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  • #3
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.
 
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  • #4
Magnetons said:
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?
 
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  • #5
... but, "If ##4^2 =15##, then you owe me $1 million" is true, then you are safe enough.
 
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  • #6
Magnetons said:
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.
:cry::cry: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.

pqp→q
TTT
TFF
FTT
FFT

Note that p→q is true except when p is true and q is false.
 
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  • #7
FactChecker said:
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😊
PeroK said:
If ##4^2 = 16##, then you owe me $1 million. True or false?
 
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Related to False. The statement does not logically follow from the given information.

What is the meaning of the statement "True or False: -1^2 = 1"?

The statement is asking whether the equation -1^2 is equal to 1. This is known as a mathematical statement or equation.

What is the order of operations for this equation?

The order of operations for this equation is to first raise -1 to the power of 2, which results in 1. Then, the negative sign is applied, resulting in a final answer of -1.

Is this statement true or false?

The statement is false. The correct answer for -1^2 is -1, not 1.

Can this statement be proven using mathematical rules?

Yes, this statement can be proven using the rules for order of operations and exponentiation. However, the answer will still be false.

Why is this statement often misunderstood?

This statement is often misunderstood because of the negative sign in front of the exponent. Many people mistakenly think that the negative sign only applies to the base number, -1, and not the entire expression. However, the negative sign applies to the entire expression, resulting in a negative answer.

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