GPT-4 Conversation #1103693695552860322

[ancient coral]

Given F(x,y,z) = (x’+y’)(x+z)

Which maxterms are included in the product of maxterms canonical representation? (Select all that apply)

0

1

2

3

4

5

6

7

[ornate lotus]

To find the maxterms included in the product of maxterms canonical representation, we'll first find the truth table for F(x, y, z):

x | y | z | F(x, y, z)

0 | 0 | 0 | (1 + 1)(0 + 0) = 2 * 0 = 0
0 | 0 | 1 | (1 + 1)(0 + 1) = 2 * 1 = 1
0 | 1 | 0 | (1 + 0)(0 + 0) = 1 * 0 = 0
0 | 1 | 1 | (1 + 0)(0 + 1) = 1 * 1 = 1
1 | 0 | 0 | (0 + 1)(1 + 0) = 1 * 1 = 1
1 | 0 | 1 | (0 + 1)(1 + 1) = 1 * 2 = 1
1 | 1 | 0 | (0 + 0)(1 + 0) = 0 * 1 = 0
1 | 1 | 1 | (0 + 0)(1 + 1) = 0 * 2 = 0

Now we'll find the maxterms:

Maxterms are included for rows where F(x, y, z) = 0, as the rows with 0 are not included in the canonical product of sum representation. In this case, rows 0, 2, 6, and 7 have F(x, y, z) = 0.

Considering these rows, the maxterms are:

M0 = (x + y + z)
M2 = (x + y' + z)
M6 = (x' + y + z)
M7 = (x' + y + z')

So the maxterms included are 0, 2, 6, and 7.

[ancient coral]

are you sure

[ornate lotus]

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[ancient coral]

Which of the following equalities are correct? (Choose all the options that are correct)

F(x,y) = (y+y')(x+0) = 1

F(A,B,C,D) = ((B+CD)A)'=B'C'+D'+A'

F(x,y) = (xy+x'y')' = x'y+xy'

F(a,b,c) = a'+b'c'+ab+ac = 1