What is the inverse of the following statement? If it is raining, then I will carry an umbrella. (1 point)

If I carry an umbrella, then it is raining.

If I do not carry an umbrella, then it is not raining.

If it is not raining, then I will not carry an umbrella.

I will carry an umbrella if and only if it is raining.

Write the following reversible statement as a Biconditional: If two perpendicular lines intersect, they form four 90° angles. (1 point)

Two intersecting lines are perpendicular if and only if they form four 90° angles.

Two intersecting, perpendicular lines do not form four angles.

Four 90° angles are formed by intersecting lines.

Perpendicular lines do not intersect.

party.girl286
Jan 23, 2018

#1**+1 **

A conditional statement is structured in the following format: \(\text{if }\underbrace{\text{hypothesis, }}\text{then }\underbrace{\text{condition}}\\ \hspace{14mm}p\hspace{29mm}q\).

1) The inverse simply negates of both the hypothesis and the condition. It is written in the following format: \(\text{if not }\underbrace{\text{hypothesis, }}\text{then not }\underbrace{\text{condition}}\\ \hspace{21mm}p\hspace{37mm}q\). In this case, the inverse of the conditional statement would read "If it is not raining, then I will not carry an umbrella. This answer corresponds with the third answer choice.

2) A biconditional statement is written in the following format: \(\underbrace{\text{Hypothesis, }}\text{if and only if }\underbrace{\text{condition}}\\ \hspace{10mm}p\hspace{45mm}q\). In this case, the biconditional statement would read "Two perpendicular lines intersect, if and only if they form four 90° angles." This answer corresponds with the first answer choice listed.

TheXSquaredFactor
Jan 23, 2018

#1**+1 **

Best Answer

A conditional statement is structured in the following format: \(\text{if }\underbrace{\text{hypothesis, }}\text{then }\underbrace{\text{condition}}\\ \hspace{14mm}p\hspace{29mm}q\).

1) The inverse simply negates of both the hypothesis and the condition. It is written in the following format: \(\text{if not }\underbrace{\text{hypothesis, }}\text{then not }\underbrace{\text{condition}}\\ \hspace{21mm}p\hspace{37mm}q\). In this case, the inverse of the conditional statement would read "If it is not raining, then I will not carry an umbrella. This answer corresponds with the third answer choice.

2) A biconditional statement is written in the following format: \(\underbrace{\text{Hypothesis, }}\text{if and only if }\underbrace{\text{condition}}\\ \hspace{10mm}p\hspace{45mm}q\). In this case, the biconditional statement would read "Two perpendicular lines intersect, if and only if they form four 90° angles." This answer corresponds with the first answer choice listed.

TheXSquaredFactor
Jan 23, 2018