Question

Select all statements that could be the first step of an indirect proof of the conditional below.

X
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If m2 = 110, then m1 = 70.
OA. Ifm22 = 110, then m1 = 70.
B. If m 21 = 70, then m 22 110.
OC. Assume if m 21 #70, then m<2 = 110.
OD. Assume if m2 = 110, then m 21 = 70.
OE. Assume if m 22 = 70, then m 21 = 110.

Answer 1

The appropriate steps for starting an indirect proof of the conditional 'If m2 = 110, then m1 = 70' would involve assuming the negation of the conclusion while keeping the premise true, and an example would be 'Assume if m2 = 110, then m1 is not equal to 70'.

Step-by-step explanation:

The question presents an indirect proof, also known as proof by contradiction, of the conditional 'If m2 = 110, then m1 = 70'. For an indirect proof, one typically assumes the opposite of what they are trying to prove and shows that this assumption leads to a contradiction.

The correct statements that could represent the first step of an indirect proof would assume the negation of the conclusion while accepting the premise as true. The appropriate options for starting an indirect proof in this case are:

• Assume if m2 = 110, then m1 ≠ 70.
• Assume m1 ≠ 70 despite m2 = 110.

The goal is to show that these assumptions lead to a logical contradiction, thereby underlining the truth of the original conditional statement. The use of modus tollens, modus ponens, and understanding valid deductive inferences is crucial in executing the proof by contradiction method effectively.