Answer:B
Step-by-step explanation:
Answer: X=-1
Step-by-step explanation:
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:
81.5, 9, 180
Step-by-step explanation:
28.
c=9
9x9=81
a=1/2
81+1/2=81.5
29.
9x1/2=4.5
4.5x2=9
30.
15x15=225
9x5=45
225-45=180
hope this helps!!!
GCF is 5m^2 n^2
m^2 has exponent 2 and n^2 has exponent 2
(1) m^5n^5
here there is no 5 so it does not have GCF
(2) 5m^4n^3
m^4 has exponent 4 greater than exponent 2
n^3 has exponent 4 greater than exponent 2
5m^4n^3 have GCF
(3) 10m^4n
10 is 5*2 . it has GCF 5
m^4 has exponent 4 greater than exponent 2
n has exponent 1 less than exponent 2
10m^4n does not have GCF
(4) 15m^2n^2
15 is 3*5 which has GCF 5
m^2 has exponent 2 which is equal to exponent 2
n^2 has exponent 2 which is equal to exponent 2
15m^2n^2 have GCF
(5) 24m^3n^4
24 is 2*2*2*3 does not have GCF
m^3 has exponent 3 greater than exponent 2
n^4 has exponent 4 greater than exponent 4
24m^3n^4 does not have GCF
