'Commutative laws' presentation slideshows

866 views • 75 slides

Clicker: Silly starter questions added January 24

Clicker: Silly starter questions added January 24. According to www.fbi.gov , How many FBI special agents are there? 572 8,192 13,890 127,736. Clicker: Silly starter questions added September 4. Approximately how many people apply for employment at the FBI each year 2500 25000 250,000

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Logical Equivalence

Logical Equivalence. Commutative laws: p ? q = q ? p, p ? q = q ? p Associative laws: (p ? q) ? r = p ? (q ? r), (p ? q) ? r = p ? (q ? r) Distributive laws: p ? (q ? r) = (p ? q) ? (p ? r) p ? (q ? r) = (p ? q) ? (p ? r)

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Set Operations

Set Operations. Section 2.2. Section Summary. Set Operations Union Intersection Complementation Difference More on Set Cardinality Set Identities Proving Identities Membership Tables. Boolean Algebra.

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Discrete Structures

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Discrete Mathematics CS 2610

Discrete Mathematics CS 2610. September 26. Equal Boolean Functions. Two Boolean functions F and G of degree n are equal iff for all (x 1 ,..x n ) ?? B n , F (x 1 ,..x n ) = G (x 1 ,..x n )

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Hardware and gates

Hardware and gates. Input signals A,B and output signal C represent individual bit values. GATE FUNCTION. A. C. C = f(A,B). F(A,B). B. Output signal from the gate. Input signals to the gate. This is a logical equation in three variable C = A and B

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Proofs Using Logical Equivalences

Proofs Using Logical Equivalences. Rosen 1.2. List of Logical Equivalences. p ?T ? p; p?F ? p Identity Laws p?T ? T; p?F ? F Domination Laws p?p ? p; p?p ? p Idempotent Laws ?(?p) ? p Double Negation Law p?q ? q?p; p?q ? q?p Commutative Laws

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Boolean Algebra

Boolean Algebra. ELEC 311 Digital Logic and Circuits Dr. Ron Hayne Images Courtesy of Cengage Learning. Inverter (Not Gate). If X = 0 then X' = 1 If X = 1 then X' = 0. AND Gate. If A = 1 and B = 1 then C = 1 (else C = 0). OR Gate. If A = 1 or B = 1 then C = 1 (else C = 0).

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Proofs Using Logical Equivalences

Proofs Using Logical Equivalences. Rosen 1.2. List of Logical Equivalences. p ?T ? p; p?F ? p Identity Laws p?T ? T; p?F ? F Domination Laws p?p ? p; p?p ? p Idempotent Laws ?(?p) ? p Double Negation Law p?q ? q?p; p?q ? q?p Commutative Laws

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LATTICES AND BOOLEAN ALGEBRA

LATTICES AND BOOLEAN ALGEBRA. Lemma:1 Show that a ?b ?a,b ?a +b for any two elements a&b in a lattice( L, ?) Proof: Let a,b ?L we know that a ?b is glb of a & b a ^b= a ?b is a lower bound of a and b ? a ?b ?a, a ?b ?b

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Boolean Algebra

264 views • 11 slides