+177 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.
+2446 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.
+2446 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.
