- #1
njama
- 216
- 1
Guys I need your help! I've never liked boolean algebra, with conjugation, disjunction, implication, equivalence and all that stuff because I considered very easy to understand.
But what I can not understand is implication (I get headaches from implications )
Here is what I do not understand.
Lets consider the following sentence:
"If at least one of the numbers a or b equals 0, then a times b equals 0"
Lets write the truth table but first...
Lets consider p - the "if" sentence, and q the "then" sentence. Its clear that we have implication because of If...then
p -----q ----- p=>q
T-------T------T
T-------F------F
F------T-------T
F------F------T
Ok that was the general case. Now let's check the "consistency" of the truth table.
For T-------T------T, at least one of a or b =0 so logically a*b would be zero.
ii) T-------F------F, at least one of a or b =0 so a*b would not be zero. (which is incorrect, therefore p=>q is false)
iii) F------T------T, (this part makes me crazy), none of a and b = 0, so a*b would be zero (which is obviously not correct but the truth table says its correct.
iv)F------F-------T, neither a or b = 0 so a*b is different from 0 (it is correct)
Am I missing some part of the sentence? Please help!
Thanks a lot.
But what I can not understand is implication (I get headaches from implications )
Here is what I do not understand.
Lets consider the following sentence:
"If at least one of the numbers a or b equals 0, then a times b equals 0"
Lets write the truth table but first...
Lets consider p - the "if" sentence, and q the "then" sentence. Its clear that we have implication because of If...then
p -----q ----- p=>q
T-------T------T
T-------F------F
F------T-------T
F------F------T
Ok that was the general case. Now let's check the "consistency" of the truth table.
For T-------T------T, at least one of a or b =0 so logically a*b would be zero.
ii) T-------F------F, at least one of a or b =0 so a*b would not be zero. (which is incorrect, therefore p=>q is false)
iii) F------T------T, (this part makes me crazy), none of a and b = 0, so a*b would be zero (which is obviously not correct but the truth table says its correct.
iv)F------F-------T, neither a or b = 0 so a*b is different from 0 (it is correct)
Am I missing some part of the sentence? Please help!
Thanks a lot.