Question

6.
Choose the best answer.

What is the inverse of:

If and , then


If then or

If or , then

If , then and

and if, and only if,
7.
Choose the best answer.

What is the contrapositive of:

If and , then


If , then and

and if, and only if,

If or , then

If then or
8.
Choose the best answer.

A statement in which a conclusion is true if the conditions of a particular hypothesis are true is called a _____ statement.

formal

conditional

deductive

valid
9.
Choose the best answer.

Is this a valid argument?

Given: If it is July 4th, then we celebrate Independence Day.

Today is July 4th.

Conclusion: Today, we celebrate Independence Day.


No. This is an improper use of the Law of Syllogism.

Yes. This argument uses the Law of Syllogism.

Yes. This argument uses the Law of Detachment.

No. This is an improper use of the Law of Detachment.
10.
Choose the best answer.

Which property is illustrated?




Commutative Property of Multiplication

Reflexive Property of Equality

Associative Property of Multiplication

Symmetric Property of Equality
11.
Choose the best answer.

What is the converse of:

If and , then


If or , then

If then or

If , then and

and if, and only if,
12.
Choose the best answer.

Which property is illustrated?




Symmetric Property of Congruence

Reflexive Property of Angles

Reflexive Property of Congruence

Transitive Property of Congruence

Answer 1

I can answer most, but Q10 and Q12 need the expressions/images that were supposed to be shown. For the others:

6) Inverse of "If p and q, then r":
- If not(p and q), then not r — equivalently: If (not p) or (not q), then not r.

7) Contrapositive of "If p and q, then r":
- If not r, then not(p and q) — equivalently: If not r, then (not p) or (not q).

8) A statement of that form is called a conditional statement.

9) Yes. This argument uses the Law of Detachment (modus ponens).

11) Converse of "If p and q, then r":
- If r, then p and q.

For 10 and 12 please paste the algebraic/equational expressions or the diagram shown with each question (the image/text that illustrates the property) and I’ll identify the correct property.