State the converse, contrapositive, and inverse of each of these conditional statements a) If it snows tonight, then I will stay at home. b) I go to the beach whenever it is a sunny summer day. c) When I stay up late, it is necessary that I sleep until noon.

Step-by-step explanation:Consider the provided information.For the condition statement [tex]p \rightarrow q[/tex] or equivalent "If p then q" The rule for Converse is: Interchange the two statements.The rule for Inverse is: Negative both statements.The rule for Contrapositive is: Negative both statements and interchange them.Part (A) If it snows tonight, then I will stay at home.Here p is If it snows tonight, and q is I will stay at home.Converse: If I will stay at home then it snows tonight. [tex]q \rightarrow p[/tex]Inverse: If it doesn't snows tonight, then I will not stay at home.[tex]\sim p \rightarrow \sim q[/tex]Contrapositive: If I will not stay at home then it doesn't snows tonight.[tex]\sim q \rightarrow \sim p[/tex]Part (B) I go to the beach whenever it is a sunny summer day.Here p is I go to the beach, and q is it is a sunny summer day.Converse: It is a sunny summer day whenever I go to the beach.[tex]q \rightarrow p[/tex]Inverse: I don't go to the beach whenever it is not a sunny summer day.[tex]\sim p \rightarrow \sim q[/tex]Contrapositive: It is not a sunny summer day whenever I don't go to the beach. [tex]\sim q \rightarrow \sim p[/tex]Part (C) When I stay up late, it is necessary that I sleep until noon.P is I sleep until noon and q is I stay up late.Converse: If I sleep until noon, then it is necessary that i stay up late.[tex]q \rightarrow p[/tex]Inverse: When I don't stay up late, it is necessary that I don't sleep until noon.[tex]\sim p \rightarrow \sim q[/tex]Contrapositive: If I don't sleep until noon, then it is not necessary that i stay up late.[tex]\sim q \rightarrow \sim p[/tex]