is p v q =(p v q) ^~(p ^q)? If so, state the truth values.
Yes, F T T F
100
Given: Candace has three apples and Christina has two apricots. If Christina has two apricots, then Colette has twelve asparagus. If Colette has twelve asparagus, then Cathy has twenty acorns. Therefore, Cathy has twenty acorns.
How many premises?
3
200
↔
What is the symbol for bi-conditional?
200
I will pass my logic test if and only if I study.
p↔s
200
Find B ∩ C
{5,7}
200
is (p ^ q) v q = q? If so, state their truth values.
Yes, T F T F
200
Given: Candace has three apples and Christina has two apricots. If Christina has two apricots, then Colette has twelve asparagus. If Colette has twelve asparagus, then Cathy has twenty acorns. Therefore, Cathy has twenty acorns.
True or false: Commutative property does not need to be used in this proof.
False
300
∩
What is the symbol for intersection?
300
Not all birds can fly.
(∃x)(Bx^~Fx)
300
Is E a subset of D?
No, 2 is not in set D.
300
is (p v q) ^ p = p? If so, state their truth values.
No, they are not logically equivalent.
300
Given:Candace has three apples and Christina has two apricots. If Christina has two apricots, then Colette has twelve asparagus. If Colette has twelve asparagus, then Cathy has twenty acorns. Therefore, Cathy has twenty acorns.
True or False: You cannot use Hypothetical Syllogism is this proof.
False, you can but you don't have to.
400
∃
What is the symbol for exixtential?
400
No students can get this problem right.
(∀x)(Sx→~Px)
400
CA (What is the compliment of A?)
{0,1,3,5,7,9}
400
Is ~(p v q) = ~p ^ ~q? If so, state their truth values.
yes, F F F T
400
Given:Candace has three apples and Christina has two apricots. If Christina has two apricots, then Colette has twelve asparagus. If Colette has twelve asparagus, then Cathy has twenty acorns. Therefore, Cathy has twenty acorns.
Complete the Proof.
1) a ^ c (given)
2) c → g (given)
3) g → n (given)
4) c ^ a (commutative)
5)c (theorem 8)
6)(c → g) ^ c (conj of 4 &5 )
7)g (MP)
8)(g → n) ^ g (conj of 3 & 7)
9) n (MP)
∴ this proof is valid!!
500
∀
What is the symbol for universal?
500
Everyone will pass their final exam.
(∀x)(Sx→Tx)
500
P(E) (power set of E?)
{},{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}
500
Is (p ^ q) v r = (p v r) ^ (q v r)? If so, state their truth values.
Yes, T T T F T F T F
500
Prove: . All Dachshunds are creatures that have back problems. All creatures that have back problems will be in pain when they're older. Princess isn't in pain when she's older Therefore Princess is not a dachshund.