if the conditional statement 'if i am 14, then i was born in 1990" is true are the converse, inverse and contrapositive also true?
2006-09-20 15:23:40 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
we are supposed to assume it is 2004 and the statement is true
2006-09-20 15:29:24 · update #1
ok if the conditional statement is true even though you could technically be born in 1989(in this scenario) and still be 14, shouldnt the others (under the same logic) be true?
2006-09-20 15:35:17 · update #2
The contrapositive is always true when the statement is. The inverse and converse may or may not be true in general. However, in this specific case they are both implied by the statement, since the only day on which that statement could be strictly true is December 31, 2004, and that it is December 31, 2004 also implies that anyone born in 1990 is 14. Note however, that it is not December 31, 2004, so the conditional statement is false.
2006-09-20 15:33:30 · answer #1 · answered by Pascal 7 · 0⤊ 1⤋
In this case the two parts of the conditional statement are identical sets: people who are 14 and people who were born in 1990, so everything is true. Normally, the first half of the statement is a subset of the second, e.g. If I am 14, then I was born in the 1990's. In those cases, only the contrapositive is true.
2006-09-20 22:36:23 · answer #2 · answered by banjuja58 4 · 0⤊ 0⤋
The converse would be if I was born in 1990 then I am 14, which would only be true if it were Dec. 31, 2004, which must be the case if the original statement is true. The contrapositive ALWAYS has the same truth value as the original, and the inverse ALWAYS has the same truth value as the converse.
2006-09-20 22:33:35 · answer #3 · answered by hayharbr 7 · 0⤊ 0⤋
I believe so...
If I am 14, then I was born in 1990.
If I am NOT 14, then I was NOT born in 1990.
If I was born in 1990 then I am 14.
If I was NOT born in 1990, then I am NOT 14.
(assuming it's 2004, and their birthday has already passed, they should all be true)
2006-09-20 22:26:59 · answer #4 · answered by goodlittlegirl11 4 · 0⤊ 0⤋
false if I was born in 1990 then I may be 13 or 14 depending on the month
2006-09-20 22:32:53 · answer #5 · answered by Bryant 1 · 0⤊ 0⤋
in this case it seems like it
but the converse of a conditional is not always true.. so be careful!
2006-09-20 22:31:30 · answer #6 · answered by Anonymous · 0⤊ 0⤋
i would say contra
2006-09-20 22:30:34 · answer #7 · answered by RichUnclePennybags 4 · 0⤊ 0⤋
no
2006-09-20 22:30:59 · answer #8 · answered by Need Help 2 · 0⤊ 0⤋