Answer:
(a) ¬(p→¬q)
(b) ¬p→q
(c) ¬((p→q)→¬(q→p))
Step-by-step explanation
taking into account the truth table for the conditional connective:
<u>p | q | p→q </u>
T | T | T
T | F | F
F | T | T
F | F | T
(a) and (b) can be seen from truth tables:
for (a) <u>p∧q</u>:
<u>p | q | ¬q | p→¬q | ¬(p→¬q) | p∧q</u>
T | T | F | F | T | T
T | F | T | T | F | F
F | T | F | T | F | F
F | F | T | T | F | F
As they have the same truth table, they are equivalent.
In a similar manner, for (b) p∨q:
<u>p | q | ¬p | ¬p→q | p∨q</u>
T | T | F | T | T
T | F | F | T | T
F | T | T | T | T
F | F | T | F | F
again, the truth tables are the same.
For (c)p↔q, we have to remember that p ↔ q can be written as (p→q)∧(q→p). By replacing p with (p→q) and q with (q→p) in the answer for part (a) we can change the ∧ connector to an equivalent using ¬ and →. Doing this we get ¬((p→q)→¬(q→p))
Answer:
x=11
Step-by-step explanation:
3x+28+5x+52+12=180
8x+92=180
-92 on both sides
8x=88
/8 on both sides
x=11
Circumference = 2πr = 2π(1.25) = 7.85ft
I hope this answers your question and best of wishes!!
Step-by-step explanation:
option A
hope it helps
thank you
Answer:
(a) 
(b) -6, 2
Step-by-step explanation:
Given: g(x) = x + 1
h(x) = (x + 6)(x - 2)
Therefore, 
(a) 
Therefore, g/h(3) = 4/9
(b) Values not in domain means we have to determine for which values of x the function becomes undefined.
This happens when the denominator becomes zero.
That means h(x) = 0
⇒ (x + 6)(x - 2) = 0
⇒ x = -6 or x = 2
Therefore, when x takes one or both of these values we can say that the function 
becomes undefined.
