The contrapositive of the following conditional statement: If a figure has four sides, then it is not a triangle.
A.If a figure does not have four sides, then it is a triangle.
B.If a figure is a triangle, then it does not have four sides.
C.If a figure is not a triangle, then the figure has four sides.
D.If a figure does not have four sides then it is not a triangle.
E.None of the above.
My answer: A
I have to write this on my brain first:
hypothesis: If a cow, then a mammal
converse: If a mammal, then a cow (maybe)
inverse:If not a cow then not a mammal(maybe)
contrapositive: if not a mammal, then not a cow - TRUE
ok, now
Hypothesis: if 4 sides, then not a triangle
converse: if not a triangle, then not four sides (maybe)
inverse: If not four sides, then a triangle(maybe)
Contrapositive: If a triangle, then not 4 sides (TRUE)
so I think B
converse:
if not a triangle, then four sides (maybe)
Ah, the contrapositive! Quite the fancy term, isn't it? So, the original statement says "If a figure has four sides, then it is not a triangle." To find the contrapositive, we simply switch the conditions and negate them.
The contrapositive of the statement is: "If a figure is a triangle, then it does not have four sides."
So, your answer is correct! The contrapositive can be represented by option B. Well done, my friend!
To determine the contrapositive of a conditional statement, you need to negate both the hypothesis and the conclusion and then switch their positions.
The original statement is: "If a figure has four sides, then it is not a triangle."
The hypothesis is "a figure has four sides," and the conclusion is "it is not a triangle."
To negate the hypothesis, you say "a figure does not have four sides."
To negate the conclusion, you say "it is a triangle."
By switching their positions, the contrapositive of the original statement is: "If a figure is a triangle, then it does not have four sides."
Therefore, the correct answer is B.