Logic & Truth Tables
Define: Disjunction
"Two statement variables that are valid when both values align as false."
Define: Existential universal statement
There is a positive integer that is less than or equal to every positive integer
If p: The cats are hungry
If q: The cats are sleepy
What is ~(p^q) in written form?
The cats are not hungry, and the cats are not sleepy.
Let A = {a, b}. List all the strings of length 3 over A that have exactly one b
aab, aba, baa
Let p = "x<3," q= "x=3," and r = "4 < x"
Write the statement in symbolic form using ^ and v symbols.
4 < x ≤ 3
r^(pvq)
Is the following statement true or false?
2 ∈ {1, 2, 3}
True.
Use DeMorgan's laws to write Negations for the statement:
-10 < x < 2
-10 > x or x >2
Fill in the black to rewrite the following statement with variables.
Is there an integer with a remainder of 1 when it is divided by 4 and a remainder of 3 when it is divided by 7?
Does there exist _____ such that if n is divided by 4 the remainder is 1 and if _____?
An integer n; n is divided by 7 the remainder is 3
Are the statements (p^q)^r and p^(q^r) logically equivalent?
Yes.
Let A = {a,b,c} and B = {u,v}
Write (A x B) x A
{((a, u)a), ((a, v)a), ((b, u)a), ((b, v)a), ((c, u)a), ((c, v)a), ((a, u)b), ((a, v) b), ((b, u)b), ((b, v)b), ((c, u)b), ((c, v)b), ((a, u)c), ((a, v)c), ((b, u)c), ((b, v) c), ((c, u)c), ((c, v)c)}