Question

the inverse ~p→~q
the contrapositive ~q→~p
the conditional statement p→q
the converse q→p

:: if you are in math class, then you are in geometry.
:: if you are not in math class, then you are in geometry.
:: if you are not in geometry, then you are not in math class.
:: if you are not in math class, then you are not in geometry.
:: if you are in geometry, then you are in math class.
:: if you are in math class, then you are not in geometry.

Explanation:

To solve this, we analyze each logical form:

1. The inverse ($\boldsymbol{\sim p \to \sim q}$)

• Let $p$ = "you are in math class", $q$ = "you are in Geometry".
• $\sim p$ = "you are not in math class", $\sim q$ = "you are not in Geometry".
• So $\sim p \to \sim q$ translates to: If you are not in math class, then you are not in Geometry.

2. The contrapositive ($\boldsymbol{\sim q \to \sim p}$)

• $\sim q$ = "you are not in Geometry", $\sim p$ = "you are not in math class".
• So $\sim q \to \sim p$ translates to: If you are not in Geometry, then you are not in math class.

3. The conditional statement ($\boldsymbol{p \to q}$)

• $p$ = "you are in math class", $q$ = "you are in Geometry".
• So $p \to q$ translates to: If you are in math class, then you are in Geometry.

4. The converse ($\boldsymbol{q \to p}$)

• $q$ = "you are in Geometry", $p$ = "you are in math class".
• So $q \to p$ translates to: If you are in Geometry, then you are in math class.

Final Matching:

• The inverse ($\sim p \to \sim q$): If you are not in math class, then you are not in Geometry
• The contrapositive ($\sim q \to \sim p$): If you are not in Geometry, then you are not in math class
• The conditional statement ($p \to q$): If you are in math class, then you are in Geometry
• The converse ($q \to p$): If you are in Geometry, then you are in math class

(Note: The other statements like "If you are not in math class, then you are in Geometry" or "If you are in math class, then you are not in Geometry" do not match any of the standard logical forms here.)

Answer:

To solve this, we analyze each logical form:

1. The inverse ($\boldsymbol{\sim p \to \sim q}$)

• Let $p$ = "you are in math class", $q$ = "you are in Geometry".
• $\sim p$ = "you are not in math class", $\sim q$ = "you are not in Geometry".
• So $\sim p \to \sim q$ translates to: If you are not in math class, then you are not in Geometry.

2. The contrapositive ($\boldsymbol{\sim q \to \sim p}$)

• $\sim q$ = "you are not in Geometry", $\sim p$ = "you are not in math class".
• So $\sim q \to \sim p$ translates to: If you are not in Geometry, then you are not in math class.

3. The conditional statement ($\boldsymbol{p \to q}$)

• $p$ = "you are in math class", $q$ = "you are in Geometry".
• So $p \to q$ translates to: If you are in math class, then you are in Geometry.

4. The converse ($\boldsymbol{q \to p}$)

• $q$ = "you are in Geometry", $p$ = "you are in math class".
• So $q \to p$ translates to: If you are in Geometry, then you are in math class.

Final Matching:

• The inverse ($\sim p \to \sim q$): If you are not in math class, then you are not in Geometry
• The contrapositive ($\sim q \to \sim p$): If you are not in Geometry, then you are not in math class
• The conditional statement ($p \to q$): If you are in math class, then you are in Geometry
• The converse ($q \to p$): If you are in Geometry, then you are in math class

(Note: The other statements like "If you are not in math class, then you are in Geometry" or "If you are in math class, then you are not in Geometry" do not match any of the standard logical forms here.)