IB Math Studies 1 Logic Test 3 Review Jeopardy
CATEGORIES:
Converse, Inverse, Contrapostive
10) State the inverse: If I do my homework, then I have an A on the test.
20) State the contrapositive: If it is snowing, then we will not have school.
30) Given….. p: I like cheese q: I like pizza. Write the following in symbols:
If I do not like pizza, then I do not like cheese.
40) Prove that the converse and inverse are logically equivalent.
Must prove using a truth table!
p
q
~p
~q
q ⇒p
(converse)
~p ⇒ ~q
(inverse)
50) Prove that the implication and the contrapositive are logically equivalent.
p
q
~p
~q
Truth Tables
10) Create a truth table for ~ p Λ ~ q
20) Create a truth table for
(p V q) Λ q
p ⇒q
~q ⇒ ~p
(implication) (contrapositive)
30) Create a truth table for ~ (p V q) Λ q
40) Create a truth table for ~ (p V q) V ~ q
50) Determine if the following are logically equivalent:
~(p Λ q) = ~p V ~q
Truth Tables Implications
10) Construct a truth table for the following
p
T
T
F
F
~ (p ↔ q)
q
T
F
T
F
20) Determine if the following are tautologies, logical contradictions, or neither. ( p V q) → ( ~p)
p
T
T
F
F
q
T
F
T
F
30) Determine if the following are tautologies, logical contradictions, or neither. (p Λ q) → (p V q)
p
T
T
F
F
q
T
F
T
F
40) Determine if the following are tautologies, logical contradictions, or neither. p Λ (p ↔ q)
p
T
T
F
F
q
T
F
T
F
50) Determine if the following are tautologies, logical contradictions, or neither.
(p → ~q) V (~p → q)
p
T
T
F
F
q
T
F
T
F
Truth Sets and Valid Arguments
10) List the truth sets for U, P, and P’ : U = { x⃓ 0 < x ≤ 18, x є N}, p: the set of prime numbers
20) List the truth sets and draw a diagram
U = { x⃓ 0 < x ≤ 20, x є N}
p: even numbers
30) Determine the validity of the argument
40) Determine the validity of the argument
q: prime numbers
50) Determine the validity of the argument
p
T
T
T
T
F
F
F
F
Venn
q
r
T
T
T
F
F
T
F
F
T
T
T
F
F
T
F
F
Diagrams
pΛq
(p Λ q) → r
(p Λ q) → r Λ p
10) Represent the following on a Venn Diagram: p Λ q
20) Represent the following on a Venn Diagram: ~p V ~q
30) Express in terms of P and Q
40) Express in terms of P and Q
50) Represent using a Venn Diagram: q V (p Λ r)
(p Λ q) → r Λ p → r