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))
What is the least common denominator used to add the fractions 1/32 and 3/24
Length
maximum: 24m
minimum: 0.1m
width
maximum: 17.2
minimum:0.1
thats all I got sorry.
Answer:
39
Step-by-step explanation:
the answer is 39 because you do 65/5 which gives you 13 and then you multiply 13 by 3. pls mark as brainliest
The vertical asymptote of f(x) is (A) x = 0, –9.
<h3>
What is a function?</h3>
- A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable).
- Functions are common in mathematics and are required for the formulation of physical relationships in the sciences.
To find the vertical asymptote of f(x):
The vertical asymptotes of a function are the zeroes of the denominator of a rational function
The function is given as:
Set the denominator to 0:
Factor out x:
Express 81 as 9^2:
Express the difference between the two squares:
Split, or or .
Solve for x:
Therefore, the vertical asymptote of f(x) is (A) x = 0, –9.
(See attachment for the graph of f(x))
Know more about functions here:
brainly.com/question/6561461
#SPJ4
The complete question is given below:
Consider the function f(x)=(x-9)/(x^3-81x) . find the vertical asymptote(s) of f(x).
A) x = 0, –9
B) x = –9
C) x = 0, 9
D) x = 9