Question

Look at the statement below.

If a number is divisible by 8, it is divisible by 4.

Which of these is a logically equivalent statement?
Choices

All numbers divisible by 4 are also divisible by 8.
If a number is not divisible by 4, it is not divisible by 8.
If a number is not divisible by 8, it is not divisible by 4.
A number is divisible by 4 if and only if it is divisible by 8.

Answer 1

@Taufique can you help me with this?

Answer 2

Well can you rule any out?

Answer 3

I think its the first time.. @natnawebb

Answer 4

?

Answer 5

first one*

Answer 6

Okay well is that true? Think of 4 itself, 4 is divisible by itself, so is 4 also divisible by 8?

Answer 7

24,28,32 <-- check these three numbers

Answer 8

YEs @natnatwebb that is true. & @experimentX ummm 4 goes into 24, 28 & 32.. But 8 doesn't go into 28..

Answer 9

that means 1) is rejected

Answer 10

similarly try to find numbers such that these hypothesis get's rejected ... don't try to prove them, just try to reject them, ... if you can't reject them, then it's your answer

Answer 11

Ohkay. can you help me with one more of these answers??

Answer 12

Hmm ... similarly if you think clearly, the last statement is also rejected. 28 is divisible by 4 but not by 8

Answer 13

Try to think for the third statement

Answer 14

I think its not THE third one.. because that doesn't seem to make sense in my min.. ;P

Answer 15

Which one would you choose @experimentX ?

Answer 16

A number (28) that is not divisible by 8, (28) is not divisible by 4
is that true??

Answer 17

nope ITS NOT

Answer 18

so its the second one right??

Answer 19

so third is also rejected... remained 2)
try to disprove 2)
"If a number is not divisible by 4, it is not divisible by 8"

Answer 20

if you cannot disprove this, then this is your answer

Answer 21

let me think for a second.

Answer 22

I cant disprove it!!!! :) so its my answer ! do you think you can help me with my LAST QUESTION.. i can post it as a new question so u can get another medal if u want:)

Answer 23

It's not the medals ... just focus on learning

Answer 24

If the weather is cold, Natalie will not go swimming.
The weather is cold, or Natalie will not go swimming.
Use the truth tables to determine whether the two statements are logically equivalent. Justify your answer.
I think they are NOT equivalent but i don't know the words to explain it!!

Answer 25

C means weather is cold .and N means natalie will not go swimming...
now,
i)logic expression of first statement C->N
ii)logic expression of second statement is C v N.
C->N is only false when N is false but C v N may be true when N is false it depends on C.

Answer 26

see arrow sign ,from the truth table it is not equivalent..