Given the true statements "if students are in grade 9, they take gym." Which statement is logically correct?
1. Bo is taking gym; therefore, she is in grade 9
2. Maria is not in grade 9; therefore, she is not taking gym.
3. Ed is not taking gym; therfore, he is taking Health.
4. Steve is not taking gym; therfore, he is not in grade 9.
I dont understand this. I used the p and q, and tried to use the "conditional" way, like if p then q. THen i used the inverse, which would give me 2. Would that be correct? If it's wrong tell me how i am wrong. =/
2007-04-05 05:30:08 · 9 answers · asked by ViVo (: 2 in Science & Mathematics ➔ Mathematics
1. False. Nothing is said about students who aren't in 9th grade but who are taking gym.
2. False. Same answer as 1.
3. False. Nothing is said about Health class.
4. True. Since all 9th graders must take gym, and Steve is not in gym, he must not be a 9th grader.
2007-04-05 05:37:44 · answer #1 · answered by Dave 6 · 0⤊ 0⤋
'if p then q' also means 'q or not p'
Let's examine the statement.
1. Bo is taking gym (q = 1), therefore she is in grade 9:
False: even if Bo is not in grade 9 (p = 0) she still may take gym
because not(p)=1 and q=1, hence not(q) or p = 1 or 1 = 1
2. Like in 1: not p does not imply not q.
3. Who mentioned Health?
4. Correct;
not p implies not q = not(not q) or not(p) = q or not p =
= p implies q.
2007-04-05 12:43:50 · answer #2 · answered by Amit Y 5 · 0⤊ 0⤋
1. Not true - True statement only says grade 9 students take gym, but doesn't exclude other grades.
2. Not true for same reason as 1.
3. Not true, as health was never a condition.
4. True, he cant be in grade 9 as true statements says if he was in 9 he'd be in gym.
2007-04-05 12:42:13 · answer #3 · answered by John B 4 · 0⤊ 0⤋
4 is the correct answer.
The condition that all 9th graders have to take gym is the defining truth. If Steve was a 9th grader, he would have to take gym. But he is not taking gym, therefore he must not be in 9th grade.
2007-04-05 12:37:00 · answer #4 · answered by trojanknight_96 3 · 1⤊ 0⤋
No clue what u talking bout p and q but answer is 4
if steve is not taking gym he aint in grade nine, because if he was in grade nine he would be taking gym
statement 1 COULD be true but it its not necessary true because she could be in grade 8 and take gym
statement 2 COULD be true also, but it is not necessarely true
statement 3 is just totaly irrelevant
2007-04-05 12:35:01 · answer #5 · answered by w1ckeds1ck312121 3 · 1⤊ 0⤋
The #4 is the correct one I think. That's my best bet. So your P & Q thing gave you the wrong answer. I'm not 100% sure though, It's been a while since I've done this stuff.
2007-04-05 12:37:55 · answer #6 · answered by Cowgirl007 2 · 0⤊ 0⤋
#4 is true.
'If p then q', so 'If not q then not p'. Applying the contrapositive rule of inference gives this result.
2007-04-05 12:48:00 · answer #7 · answered by firstythirsty 5 · 0⤊ 0⤋
I also think it is #4.
2007-04-05 12:35:59 · answer #8 · answered by RogerDodger 1 · 1⤊ 0⤋
The answer is the 4th one.
2007-04-05 12:43:09 · answer #9 · answered by jewls_1_3 2 · 0⤊ 0⤋