Question

a.) Determine if a' + a'y = a' using a truth table. DO NOT REFER TO THE FORMULA SHEET. This must be proved via truth table.

Use the table tool, to create your truth table. If you are unable to use the table tool, you can use excel or word to create the table and copy paste. Be sure to write a statement indicating that this is true or not.

b.) Given that x + 1 = 1 is true. Find it's dual. (use duality)

a.) x1=1

b.) x + 0 = x

c.) None of the above

d.) x0 = 0

e.) x + 0 = 0

Answer 1

a.) To determine a' + a'y = a' using truth table, lets make the truth table and check whether the values in the columns of a' + a'y and a' are same or not. If they are same, then the given expression is valid, otherwise not.

a	y	a'	a'y	a' + a'y
0	0	1	0	1
0	1	1	1	1
1	0	0	0	0
1	1	0	0	0

Since the values in the columns of a' and a' + a'y are same, hence the expression is valid.

Hence, a' + a'y = a' is true.

b.) Dual of an expression can be found by replacing AND with OR, OR with AND, + with . , . with + and 0 with 1 and vice-versa.

Hence, the dual of x + 1 = 1 will be d.) x0 = 0

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