How to prove logic expressions with numbers in them with truth table

Question

I'm studying logic gates and expressions using truth tables and I'm really struggling with the concept. Here's on assignment I have and it would really help if I can see an example on how to go about solving these kind of examples. The assignment is to prove that this statement is right using a truth table. A(1+ ¬AC)+ ¬A = 1 Any help would be greatly appreciated with this! Thanks in advanced for taking the time to help.

Answer 1

Filling in the truth table is a straightforward task, but keep in mind 1 + anything = 1 and A + ¬A = 1 as you fill in:

A C ¬A  ¬AC   1+¬AC  A(1+¬AC) A(1+¬AC)+¬A
0 0 
0 1
1 0
1 1

Try filling in one column at a time and if everything goes right, you must see all 1s in the last column.

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Filling in the table you should get

A C ¬A  ¬AC   1+¬AC  A(1+¬AC) A(1+¬AC)+¬A
0 0  1   0     1        0        1
0 1  1   1     1        0        1
1 0  0   0     1        1        1
1 1  0   0     1        1        1