# Math

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Part 1: Write two conditional statements for which the converse is true.

1. Statement:
2. Converse:

3. Statement:
4. Converse:

Part 2: Write two conditional statements for which the converse is false.

5. Statement:
6. Converse:

7. Statement:
8. Converse:

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• Math - ,

I assume you have a basic background in symbolic logic, which helps in solving this kind of problems.

The difference between the two kinds of statements is
A. if statements where the converse is true is of the form:
p <-> q, which has the same truth table as
p->q ∧ q->p

B. if statement where the converse is not (always) true is of the form:
p->q

Statements of type B are encountered more frequently in life, such as:

p->q
"If it rains(p), the street is wet(q)."

The converse is
q->p
"If the street is wet, it rains."

Statements of type A are more like equivalent statements than if statements:

p<->q ≡ (p->q)∧(q->p)
p->q: "If I am a member(p), I pay my dues(q)"
q->p: "If I pay my dues, I am a member".

"If the street is wet