discrete assignment 1(a)
DESCRIPTION
Discrete Assignment 1(a)Discrete Assignment 1(a)Discrete Assignment 1(a)Discrete Assignment 1(a)Discrete Assignment 1(a)TRANSCRIPT
Logical Operators
1) Negation (~, πππ‘)
Let βπβ be a proposition. The Negation of βpβ denoted by "~π".
πβπ ππππ’π ππ β~πβ ππ π‘βπ πππππ ππ‘π ππ π‘βπ π£πππ’π ππ βπβ
πππ’π‘β πππππ ππ πππππ‘πππ
π ~π
1 0
0 1
2) Conjunction (β, πππ)
Let βπβ and βπβ b two propositions. The conjunction of βπβ and βπβ denoted by "π β π".
"πβπ πΆππππ’πππ‘πππ "π β π" ππ π π€βππ πππ‘β βπβ πππ βπβ πππ π ππ‘βπππ€ππ π π"
πππ’π‘β πππππ ππ πΆππππ’πππ‘πππ
π π π β π 1 1 1
1 0 0 0 1 0
0 0 0
3) Disjunction (β, ππ)
Let βπβ and βπβ b two propositions. The disjunction of βπβ and βπβ denoted by "π β π".
"πβπ π·ππ ππ’πππ‘πππ "π β π" ππ π π€βππ ππ‘ ππππ π‘ πππ ππ βπβ πππ βπβ ππ π ππ‘βπππ€ππ π π"
πππ’π‘β πππππ ππ π·ππ ππ’πππ‘πππ
π π π β π 1 1 1
1 0 1 0 1 1
0 0 0
4) Implication (Conditional) (β, πππππππ )
Let βπβ and βπβ b two propositions. The conditional statement of βπβ and βπβ denoted by "π β π".
"πβπ πΆππππππ‘πππππ ππ‘ππ‘πππππ‘ "π β π" ππ π π€βππ βπβ ππ π πππ βπβ ππ π ππ‘βπππ€ππ π π"
πππ’π‘β πππππ ππ πΌπππππππ‘πππ
π π π β π 1 1 1
1 0 0 0 1 1
0 0 1
5) Bi-implication (bi-conditional) (β, ππ πππ ππππ¦ ππ)
Let βπβ and βπβ b two propositions. The bi-conditional statement of βπβ and βπβ denoted by "π β π".
"πβπ π΅π β πππππππ‘πππππ ππ‘ππ‘πππππ‘ "π β π" ππ π π€βππ πππ‘β βπβ πππ βπβ βππ£π π πππ π£πππ’π
ππ‘βπππ€ππ π π"
πππ’π‘β πππππ ππ π΅π β ππππππππ‘πππ
π π π β π 1 1 1
1 0 0 0 1 0
0 0 1
6) Exclusive or (β¨, ππ₯ ππ)
Let βπβ and βπβ b two propositions. The exclusive or of βπβ and βπβ denoted by "π β¨ π".
πβπ πΈπ₯πππ’π ππ£π ππ π β¨ π" ππ π π€βππ ππ₯πππ‘ππ¦ πππ ππ βπβ πππ βπβ ππ π ππ‘βπππ€ππ π π"
πππ’π‘β πππππ ππ πΈπ₯πππ’π ππ£π ππ
π π π β¨ π 1 1 0
1 0 1 0 1 1
0 0 0
7) NAND Logical Operator (β)
Let βπβ and βπβ b two propositions. The NAND of βπβ and βπβ denoted by "π β π".
πβπ ππ΄ππ· "pβq" ππ π ππ πππ‘β ππ ππ‘π ππππππ‘πππ βπβ πππ βπβ πππ π ππ‘βπππ€ππ π π
πππ’π‘β πππππ ππ ππ΄ππ·
π π π β π 1 1 0
1 0 1 0 1 1
0 0 1
8) NOR Logical Operator (β)
Let βπβ and βπβ b two propositions. The Nor of βπβ and βπβ denoted by "π β π".
πβπ πππ "pβq" ππ π πππππ‘β ππ ππ‘π ππππππ‘πππ βπβ πππ βπβ ππ π ππ‘βπππ€ππ π π
πππ’π‘β πππππ ππ πππ
π π π β π 1 1 0
1 0 0 0 1 0
0 0 1