Logic and Conditional Statements

Match the statement with the symbolic notation.

Conjunction

• q → p

• p ↔ q

• p ∨ q

• p ∧ q

• ~q → ~p

Answer explanation

remember - conjunction is an AND statement which is symbolized by an upside down V (or a capital A without the line across).

Match the statement with the symbolic notation.

Disjunction

• q → p

• p ↔ q

• p ∨ q

• p ∧ q

• ~q → ~p

Answer explanation

remember - disjunction is an OR statement, which is represented by a V.

Match the statement with the symbolic notation.

Conditional

• q → p

• p ↔ q

• p → q

• ~q → ~p

• ~p → ~q

Answer explanation

remember - conditional is an "if, then" statement meaning "if p, then q"

Match the statement with the symbolic notation.

Inverse

• q → p

• p ↔ q

• p → q

• ~q → ~p

• ~p → ~q

Answer explanation

remember - inverse is the conditional statement negated, so "if not p, then not q".

Match the statement with the symbolic notation.

Converse

• q → p

• p ↔ q

• p → q

• ~q → ~p

• ~p → ~q

Answer explanation

remember - converse is found by switching the conditional, so "if q, then p".

Match the statement with the symbolic notation.

Contrapositive

• q → p

• p ↔ q

• p → q

• ~q → ~p

• ~p → ~q

Answer explanation

remember - contrapositive is found by switching and negating the conditional, so "if not q, then not p".

Match the statement with the symbolic notation.

Biconditional

• q → p

• p ↔ q

• p → q

• ~q → ~p

• ~p → ~q

Answer explanation

remember - biconditional is "p if and only if q", and is only true when both the conditional and converse are BOTH true.

Decide whether the following is using Law of Detachment or Law of Syllogism.

Given - If Andrew runs a mile in under 5 minutes, then he will have a new personal record.

Given - Andrew Ran a mile in 4 minutes and 50 seconds.

Conclusion - Andrew has a new personal record.

• Law of Detachment

• Law of Syllogism

Using the Law of Syllogism, does the following create a valid conclusion?

Given - If you go to the water park, then you will need to bring sunscreen.

Given - If you do not bring sunscreen, then you will burn.

Conclusion - If you go to the water park, then you will burn.

• Yes, valid conclusion

• No, invalid

Identify the hypothesis and conclusion of the conditional statement.

If it is daylight savings time, then I must reset my clocks.

• Hypothesis - If it is daylight savings time

  Conclusion - Then I must reset my clocks

• Hypothesis - If I must reset my clocks

  Conclusion - then it is daylight savings time

• Hypothesis - It is daylight savings time

  Conclusion - I must reset my clocks

• Hypothesis - I must reset my clocks

  Conclusion - It is daylight savings time

Answer explanation

Remember, hypothesis comes after "if" (does not include if) and conclusion comes after "then" (does not include then)