Question

Conventially, the converse isn't true, right?

Answer 1

the rule is that only the contrapositive is equivalent to its conditional statement...

Answer 2

Talking to @jazy and @sauravshakya in the math chat, I found out a counterexample: “If a student is \(\rm x\) years old, then he is in grade \(\rm x + 5\).”

Answer 3

mmhmm

Answer 4

and?

Answer 5

The contrapositive is true!
If a student is not in grade \(\rm x + 5\), then he is not \(\rm x\) years old.

Answer 6

yes. that's what i said

Answer 7

Yeah, so the contrapositive is equivalent to the conditional, and the converse is true.

Answer 8

the only time the converse is true is when the statement is biconditional

Answer 9

converse is not equivalent to the conditional

Answer 10

How so?

Answer 11

I mean, isn't what I said true?

Answer 12

p q p -> q q -> p
T T T T
T F F T
F T T F
F F T T

not equivalent

Answer 13

I mean that... here, p -> q is also true and q -> p is also true.

Answer 14

\[q \rightarrow p \equiv p \rightarrow q\]
\[\neg q \vee p \equiv p \rightarrow q\]
\[p \vee \neg q \equiv p \rightarrow q\]
\[\neg(\neg p) \vee \neg q \equiv p \rightarrow q\]
\[\neg p \rightarrow \neg q \equiv p \rightarrow q\]
see how they're not equivalenT/

Answer 15

anyway....you were saying?

Answer 16

Wait, where exactly is the fallacy?

Answer 17

“If a student is x years old, then he is in grade x+5" is not the same as "If a student is in grade x + 5, then he is x years old"

Answer 18

Yes, it is...

Answer 19

q -> p is equivalent to ~p-> ~q not p->q

Answer 20

If we kick the truth tables out, then they essentially mean the same.

Answer 21

logical equivalence are not the same either

Answer 22

and like i said... “If a student is x years old, then he is in grade x+5" is not the same as "If a student is in grade x + 5, then he is x years old"

Answer 23

wanna see how?

Answer 24

in a way...you can call it a counter-counterexample