Question

Write a statement that is logically equivalent to the statement below. Demonstrate it is logically equivalent by citing evidence to justify your statement:

If today is a weekday, then it is not Saturday.

Answer 1

will give medal if you get it correct and will fan

Answer 2

Make a converse or contrapositive of the statement. If one of them still makes sense, it is logically equivalent

Answer 3

ok

Answer 4

okay so my converse would be If it is not Sunday, then it is a weekday. right?

Answer 5

Incorrect, because it could be Saturday which would not be a weekday, not is it Sunday.

Answer 6

use the contrapositive

Answer 7

ok

Answer 8

If it is not Saturday, then it is not a weekday.

Answer 9

original statement: if p , then q.
If today is a weekday, then it is not Saturday.

contrapositive : if not q, then not p .
If it is not not saturday, then today is not a weekday.

Answer 10

there are two 'not' parts

Answer 11

two 'not's make an 'is'
For example :
It is not the case that i not going to the store.
This is equivalent to going to the store.

Answer 12

original statement: if p is the case , then q is the case.
If it is the case that today is a weekday, then it is the case that it not Saturday.

contrapositive : if q is not the case, then p is not the case.
If it is not the case that it is not Saturday, then it is not the case that today is a weekday.

Answer 13

if it is not the case that it is not saturday, that is the same thing as saying it is saturday

Answer 14

im confused now...

Answer 15

Let's symbolize the statement using letters p,q.
p = 'today is a weekday'
q = 'it is not saturday'
So the original statement is
if p , then q

Answer 16

do you agree so far?

Answer 17

original statement:
If today is a weekday (p), then it is not saturday (q).
We can abbreviate this as
If p , then q.
We'll see later why we want to abbreviate, it makes it easier to find the logical equivalent expressions.