Question

which of the following is true

Answer 1

I see two correct answers...

Answer 2

okay ..
which one and how plse explain

Answer 3

p, q, and r are all true, right?

Answer 4

okay

Answer 5

any idea

Answer 6

if p and q is true... then... p and q is true LOL

Answer 7

So that means
\[\huge (p\land q)\] would be correct.

Answer 8

Hello...?

Answer 9

Is that so?

Answer 10

I mean, p, q, and r, are all true.

Answer 11

p statement is "4 is an even number"
which is true... therefore p is true.

Answer 12

I guess so?

Answer 13

Actually, you can... that's called Logical Conjunction...
\[P\\Q\\\therefore P\land Q\]

Answer 14

It doesn't matter.
My point is, we are given these...
\[P\\Q\\R\]
And logically we can conclude
\[P\land Q\]

I am not saying this is the only conclusion, but this is A correct conclusion to draw, nevertheless.

Answer 15

We are not asked to form a tautology, we are merely asked which of the four choices is true.

Answer 16

Excuse me?

Answer 17

It's okay.

Answer 18

This comes from a misunderstanding. I withhold my statement until @msingh clears this up.
But I firmly stand by my interpretation that
p is the variable representing the statement "4 is an even number"
(implying p is true)
and so on.

Answer 19

Then, please, next time, do not be so quick to judge other people's reasoning as ridiculous, particularly if you do not know the answer yourself, and regardless, it is simply not polite.

Answer 20

friends plse cooperate , we here are to study and help each other , plse i request both of u

Answer 21

@msingh
You're here after all...
Perhaps you can clear this up... what exactly are p, q, and r?

Answer 22

i really don't know
i want to also clear this query asap

Answer 23

@hoa , i know

Answer 24

Perhaps you can show me a sample problem which is similar, and with its answer.

Answer 25

this is the main pblm , i didn;t get anything simialr to it

Answer 26

@Hoa I still do not fancy my reasoning being called ridiculous.

Answer 27

Is there only one answer, @msingh ?

Answer 28

yes

Answer 29

Let me just rewrite it here...

If
p: 4 is an even number
q: 6 is a divisor of 12
r: HCF of 4 & 6 is 2

then which of the following is true?
\[\large a) \quad (p\land q)\\ \large b)\quad (p\lor q)\land \lnot \ r\\\large c)\quad \lnot \ p\lor (q\land r)\\\large d) \quad \lnot \ (q\land r)\lor p\]

Answer 30

So, @msingh my question, mainly, is that, are p, q, and r taken to be variables representing the statements adjacent to them?
Namely that
p is the the statement "4 is an even number" ?
etc

Answer 31

yes

Answer 32

Well, that does pose a problem, see, with that logic, all but (b) are true....

Answer 33

Take for instance, (a)
4 is an even number AND 6 is a divisor of 12...
The statement is true, no?

Answer 34

okay

Answer 35

as for (b)
(4 is an even number OR 6 is a divisor of 12) AND 2 is not the HCF of 4 and 6

Answer 36

okay

Answer 37

well, what can you say about statement (b) ?

Answer 38

hmm, i got it

Answer 39

Well?

Answer 40

b) option is answer

Answer 41

But I thought you were being asked which statement was true? And (b) is false...

Answer 42

kk

Answer 43

unfortunately, a, c, and d all seem to be true...

Answer 44

so which one is true

Answer 45

okay

Answer 46

And there's my problem, unless you can clear that up with a previous and similar item... sorry :)

Answer 47

its okay bro,