Answer:
<h3>Required <u>Answer</u><u>:</u><u>-</u></h3>
- by adding eq (1) and eq (2) we get
<h2>__________________________</h2>
- Substitute the value in eq (2)
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))
She would have 4/5 dog toys that are left. So about 40 dog toys.
Hope this would work and help!
Least Common Multiple (LCM) of 4 and 8 is 8. 4 is 2 x 2, while 8 is 2 x 2 x 2. We take the first two that's shared, second two's that shared, and third two that's note. We have three twos, or 2 x 2 x 2 = 8. So the LCM of 4 and 8 is 8.
