Boolean Algerbra

mickeyraes

Can anyone explain how to work this out?.

A B A & & b (AND)
False False False
False True False
True False False
True True True

Using the above information what is the result of the following statement?

(2<3) AND (3<4)

A. True
B. False

Razzen

Ok you've a truth table for logical AND, which lists all possible combinations of A and B

The first line of your table could be read as:
if some condition A is false and some condition B is also false the the result of A && B will also be false.

so now you are being asked to use the truth table to work out the answer to
(2<3) AND (3<4)

So (2<3) would be A in our table and (3<4) would be B

So is A true or false? is 2<3? yes so A = True
and is B true of false? is 3<4? yes so B = True

we can now look at the last line of the truth table to see that when A is true and B is true then A && B is also true.

The key is understanding that the truth table gives us all possible combinations, and we can then use it to evaluate any equation using AND.

Hope that helps a little.

mickeyraes

Thanks Razzen, well explained have another one for you:

A B A B | | (OR)
False False False
False True True
True False True
True True True

Using the above information what is the result of the following statement

(4 = = 5) | |( 2 + 2 = =4)

a. true
b.false

Razzen

There should be enough info in my first post for you to try answer this one... Give it ago and post up your attempt..i'll help once you've made an attempt at it yourself.

mickeyraes

Would the answer be true. The first one (4==5) is false and the second one (2+2==4) is true

Razzen

Yup well done....

Basically For AND the answer is only ever true if both A AND B are true

for OR, the answer is true is A OR B is true (if they are both true then that's also good)

XOR would mean strictly A OR B (but not both)

Good luck with them.