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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.

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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]

The converse, contrapositive, and inverse of each of the specified conditional statements are shown below.

How to form converse, contrapositive, and inverse of conditional statement?

Suppose the conditional statement given is:

[tex]p \rightarrow q[/tex] or 'if p then q'

Then, we get:

  • Converse: "if q then p" or [tex]q \rightarrow p[/tex]
  • Contrapositive: "if not q then not p" [tex]\sim q \rightarrow \sim p[/tex]
  • Inverse: "If not p then not q" [tex]\sim p \rightarrow \sim q[/tex]

For the listed conditional statements, finding their converse, contrapositive, and inverse statements:

  • Case 1: If it snows tonight, then I will stay at home.
  1. Converse : If i will stay at home, then it snows tonight.
  2. Contrapositive : If i don't stay at home, it won't snow tonight.
  3. Inverse : If it doesn't snow tonight, then i will not stay at home.

  • Case 2:  I go to the beach whenever it is a sunny summer day

This can be taken as: If it is a sunny summar day, then i go to the beach.

  1. Converse : If i go to the beach, then it is a sunny summer day.
  2. Contrapositive : If i do not go to the beach, then it isn't a sunny summer day
  3. Inverse : If it's not a sunny summar day, then i do not go to the beach.

Learn more about converse, contrapositive, and inverse statements here:

https://brainly.com/question/13245751?referrer=searchResults

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