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II - OR (Logical Disjunction)
This operator can be represented by the symbol " ". A
least 1 of n operands is TRUE, if n operands are FALSE, then the result is FALSE.
Main properties:
• Commutativity:
A∨(B∨C )⇔( A∨ B)∨C
• Associativity:
A∨(B∧C )⇔(A∨ B)∧( A∨C )
• Distributivity:
Input Output
A B
0
0
1
1
III -
XOR (Exclusive disjunction)
This operator can be represented by the symbol "⊕". A n-place logical operator XOR results TRUE if one
odd number of operands is TRUE, otherwise the result is FALSE.
Main properties:
• Commutativity:
A⊕( B⊕C)⇔( A⊕B)⊕C
• Associativity:
User's Manual
A∨ B⇔ B∨ A
;
Table 11: Truth tables for Disjunction Operation
A∨B
A B C A∨B C
0
0
0 0 0
1
1
0 0 1
0
1
0 1 0
1
1
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
A⊕ B⇔ B⊕ A
;
n-place logical operator AND results TRUE if at
∨
;
;
Output
Input
A B C D A∨B C D
∨
0
0 0 0 0
1
0 0 0 1
1
0 0 1 0
1
0 0 1 1
1
0 1 0 0
1
0 1 0 1
1
0 1 1 0
1
0 1 1 1
1 0 0 0
1 0 0 1
1 0 1 0
1 0 1 1
1 1 0 0
1 1 0 1
1 1 1 0
1 1 1 1
;
Appendixes
Output
∨ ∨
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Page 41
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