Recall that a ⇒ b ≡ ¬a ∨ b.
• r ⇒ (p ∧ q) ≡ ¬r ∨ (p ∧ q)
In row C, q is false so p ∧ q false, and r is true so ¬r is false.
¬r ∨ (p ∧ q) ≡ false ∨ false ≡ false
• r ⇒ (p ∨ q) ≡ ¬r ∨ (p ∨ q) = p ∨ q ∨ ¬r
In each of rows A, C, and E, at least one of p or q is true, so
p ∨ q ∨ ¬r = true
• (q ∧ r) ⇒ p ≡ ¬(q ∧ r) ∨ p ≡ (¬q ∨ ¬ r) ∨ p = p ∨ ¬q ∨ ¬r
In row E, p is false and both q and r are true, so ¬q and ¬r are both false.
false ∨ false ∨ false = false
• (q ∨ r) ⇒ p ≡ ¬(q ∨ r) ∨ p ≡ (¬q ∧ ¬r) ∨ p
In row E, p is false and both q and r are true, so both ¬q and ¬r are false.
(¬q ∧ ¬r) ∨ p ≡ (false ∧ false) ∨ false ≡ false ∨ false ≡ false
Answer:
14% discount
Step-by-step explanation:
I was off by 2%
Answer:
Integer 1 is x
Integer 2 is y
x + y = -31
x - y = -55
Add:
2x = -86
x = -43
Substitute:
-43 + y = -31
y = 12
Therefore, the two integers are: 12 and -43
Answer:
Total number of orange trees = 77 trees
Step-by-step explanation:
Given:
Total number of rows = 15
Total number of cherry rows = 4
Number of trees in each rows = 7
Find:
Total number of orange trees
Computation:
Total number of orange trees = [Total number of rows - Total number of cherry rows][Number of trees in each rows]
Total number of orange trees = [15 - 4]7
Total number of orange trees = [11]7
Total number of orange trees = 77 trees
