00:00ABC are positive numbers that are not zero.
00:02The equations A multiplied by 1/2, C multiplied by 3, and A equals 3/2 times C are given.
00:07Our question asks which of the following is true.
00:11Now we know, friends, that here we are given both true and false antithesis premises, right friends?
00:17Yes.
00:17Which one is the correct antithesis, and which one is the opposite antithesis?
00:19Let's consider X and Y.
00:23Let's say for X and Y.
00:27If Y equals K times X, then what is K here, folks?
00:31That was our constant of proportionality.
00:33So, if Y divided by X equals K, what was that again, guys?
00:40Direct proportion.
00:42So, if Y equals K divided by X, and K is our constant of proportionality, what was it again, folks?
00:50If X times Y equals K, then what is that?
00:53It was an inverse relationship.
00:55Let's take a look at this, folks.
00:57Let's look at A.
00:59It says that A and B are directly proportional.
01:00So, what does A times B equal to 1 divided by 2 mean, guys?
01:03In terms of coefficient.
01:04So it's equal to our ratio of proportion, our constant of proportionality.
01:09In this case, what is A times B, guys?
01:11It's an inverse proportion because it's a multiplication situation.
01:15Let's look at B.
01:18He says that B and C are inversely proportional.
01:20Now, in order to find B and C, so that we can put them into a division or multiplication situation,
01:25Instead of A, we need to use the equation 3 divided by 2 times C.
01:293 divided by 2 times C times, here I'm putting the first equals sign, friends.
01:35What was it?
01:36B.
01:36That's equal to 1/2.
01:37So again, it's just that here, friends C and B are in a multiplication situation,
01:42What is C times B, folks?
01:45Because it is 1/3,
01:51What is this place, guys?
01:53Of course, it's inversely proportional.
01:55So, this option is actually correct.
01:57But I'd still like to look at options C, D, and E as well.
02:00What do your friends say in option C?
02:02It says that A and D are directly proportional.
02:05There's an A here, right guys?
02:08It says 3 divided by 2 times C.
02:10What did he say here?
02:11D.
02:12Here you go, friends,
02:14Instead of C, I say,
02:16What should happen?
02:17C times B is 1/3, we found the whole number.
02:20Instead of C, friends,
02:21I'm writing 3 divided by D.
02:27A equals 3/2 times 3/D.
02:33Isn't that correct in our third equation?
02:35Yes.
02:36When I perform subtraction,
02:382 times A times D,
02:40That equals 9.
02:41A times D from here,
02:44The proportionality constant is equal to 9 divided by 2.
02:47Isn't this a case of A times D?
02:49Are they directly proportional?
02:50No, they are inversely proportional.
02:52This isn't it, folks.
02:54That's not it either.
02:55Our answer will be B.
02:56I'd like to look at D as well.
02:58My friends say that A and C are inversely proportional.
03:01Now, so that we can place A and C next to each other, friends,
03:06What did we put in place of B here?
03:08When we find it over there, right over there,
03:12Wasn't it 1 divided by 3 times C?
03:15When we do it here,
03:16C times 1 divided by,
03:18B equals.
03:18We can also write it as 1/3 multiplied by C.
03:21In this situation,
03:22Instead of A multiplied by B,
03:24We were equal at first,
03:25When I put 1/3 times C,
03:27And that's what I meant when I said 1/2,
03:30When I perform subtraction,
03:32I don't even need to.
03:33A times 1 divided by 3 times C,
03:35I'll transfer this account for nothing.
03:37Aren't these in episode format?
03:38It's A divided by C.
03:39So what is this, guys?
03:40They are directly proportional.
03:43That's not it either.
03:45He says that B and D are inversely proportional.
03:48Option E.
03:49Let's look at B and D, guys.
03:52Now, in B and D,
03:55Let's consider this C times D.
03:58In C times D, C equals,
04:003 divided by D, right guys?
04:05When I look over here, my friends,
04:093 divided by D times B equals,
04:121 in 3.
04:13What about B and D?
04:14Friends, this is a chapter situation.
04:16When we multiply and divide from here,
04:17This is actually,
04:19that it is directly proportional,
04:21We find B and D.
04:22So, which is our answer in this case, friends?
04:24The part about B and C being inversely proportional is true.
04:27Our answer is the Bolu option.
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