TRUTH TABLES

Question 1

Truth Table for ∧

Answer 1

α β | (α ∧ β)
1 1 | 1 Only true when both α β are true
1 0 | 0 False in every other case
0 1 | 0
0 0 | 0

Question 2

Truth Table for ∨

Answer 2

α β | (α ∨ β)
1 1 | 1 True if at least one input is true
1 0 | 1
0 1 | 1
0 0 | 0 Only false when both α β are false

Question 3

Truth Table for ¬

Answer 3

α | ¬α
1 | 0
0 | 1

Question 4

Truth Table for ⊕

Answer 4

α β | (α ⊕ β)
1 1 | 0 Only false when both α β are false or true
1 0 | 1 True if one input is true
0 1 | 1
0 0 | 0

Question 5

Truth Table for ↓ (NOR)

Answer 5

α β | (α ↓ β)
1 1 | 0 False if at least one input is true
1 0 | 0
0 1 | 0
0 0 | 1 Only true when both α β are false

Question 6

Truth Table for ↑ (Nand/Sheffer stroke)

Answer 6

α β | (α ↓ β)
1 1 | 0 Only false when both α β are true
1 0 | 1 True if at least one input is false
0 1 | 1
0 0 | 1

Question 7

Truth Table for ⊥

Answer 7

/ | ⊥
/ | 0 (No inputs and False)

Question 8

Truth Table for ⊤

Answer 8

/ | ⊤
/ | 1 (No inputs and True)