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.

Answer 1

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.

Answer 2

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.

Answer 3

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.