Truth table to prove an argument true/false

Question

Can someone help me out with truth tables? I would like to create a truth table to prove whether or not this is true.

Is this homework? If so, please tag it so. – Ted Hopp Mar 06 '11 at 05:15 — Ted Hopp, Mar 06 '11 at 05:15

score 0 · Answer 1 · answered Mar 06 '11 at 05:13

0

A = 0, B = 0, C = 0
A ∨ (B ∧ C) = 0 ∨ (0 ∧ 0) = 0 ∨ 0 = 0
(A ∨ B) ∨ (A ∧ C) = 0

Do the similar for the 7 more combination of A, B and C.

A = 0, B = 0, C = 1
A = 0, B = 1, C = 0
//// etc.

If you find both end same for all the eight then that is proved. Otherwise the are not same.

Also visit the Wikipedia entry for truth table for the details. Application section contains an example proof of another equation.

Note: Sounds like a homework. So not providing the full solution.

answered Mar 06 '11 at 05:13

taskinoor

45,586
12
116
142

thx, this is actually for demonstration that I need to present to co-workers.. Unfortunately I am not that hip on truth tables so that makes it a bit difficult :) – user646672 Mar 06 '11 at 05:14
Cheek the Wikipedia link that I have added. That may help you further. – taskinoor Mar 06 '11 at 05:18

Prasoon Saurav · Accepted Answer · 2011-03-06T05:26:39.163

A  B  C    B∧C   A∨(B∧C)  A ∨ B   A ∧ C    (A ∨ B) ∨ (A ∧ C)
0  0  0     0       0        0        0               0
0  0  1     0       0        0        0               0
0  1  0     0       0        1        0               1 
0  1  1     1       1        1        0               1 
1  0  0     0       1        1        0               1
1  0  1     0       1        1        1               1
1  1  0     0       1        1        0               1
1  1  1     1       1        1        1               1

When A=0, B=1 and C=0

A ∨ (B ∧ C) = 0
(A ∨ B) ∨ (A ∧ C) = 1 ∨ 0 = 1

So A ∨ (B ∧ C) = A ∨ B) ∨ (A ∧ C) is false.

Awesome! so 0 being false and 1 being true? – user646672 Mar 06 '11 at 05:21 — user646672, Mar 06 '11 at 05:21

score 0 · Answer 3 · answered Mar 06 '11 at 05:19

You only have three boolean variables, which means a 2^3=8 entry truth table will suffice. I suggest breaking down columns in your table to produce one boolean result at a time. If the two columns of the two sides of your boolean equation match, them you proved they are the same, otherwise you will have one or more counter-examples.

If the two expressions match, then you can try to prove they are equal using the rules of Boolean algebra. Karnaugh maps could even be used to point the way.

Truth table to prove an argument true/false

3 Answers3