WGU C959 - Discrete Math

WGU C959 - Discrete Math 5.0 (2 reviews) Students also studied Terms in this set (142) Western Governors UniversityMATH 2800 Save Discrete Flashcards 37 terms ashenderson4372 Preview

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A = { 3, 4, { 3, 4 }, { 1, 2, 3 }, 5 }

{ 3 } ⊆ A

True or False What is the notation for subset?⊆ A collection of objects is known as aset What is the notation for integers?ℤ What is the notation for element?∈ Choose an answer 1True2False Don't know?

What is the notation for set-roster?{ } Write the set-builder notation for, "Numbers whose square roots are an integer" { x | √x ∈ ℤ} Write the set-builder notation for "the set of all x's, such that x is greater than 0" { x | x > 0}

T/F:

Order matters in ordered pairs?True In a Cartesian Product of two sets, every element of the CROSS PRODUCT is an ordered pair

What is the Cartesian Product for:

{a,b} x {0,1} A x B = { {a,1} , {a,0} , {b,1} , {b,0} } Ordered pairs are _____ of the Cartesian Product elements A ______ is a subset between two different setsrelation Give the general equation for Relations(a,b) ∈ A x B (i.e. (a,b) is the ordered pair and A x B are two different sets) Describe in words what this formula means: (a,b) ∈ A x B Ordered pair (a,b) are in the two sets A x B True ∧ True =True True ∧ False =False False ∧ False =False True ∨ False =True True ∨ True =True False ∨ False =False A compound proposition is a tautology if the proposition is always _____ True A compound proposition is a contradiction if the proposition is always _____ False If p is False and q is True, solve this equation.p → q True

If an equation is show as this "p → q" and the hypothesis is false, then the answer to the question is _____ True Give the truth table for ¬(p ↔ q)F T T F What is the logical equivalence of ¬(p ∧ q) ≡ ?(¬p ∨ ¬q) What is the logical equivalence of ¬(p ∨ q) ≡ ?(¬p ∧ ¬q) What is the logical equivalence of p→q ≡ ?(¬p ∨ q) In Boolean Algebra the addition symbol is the same as what?

OR The XOR operation outputs 1 when what?Both inputs are different

(1 XOR 0 = 1)

(1 XOR 1 = 0)

Boolean multiplication is the same as what?AND The minterm must evaluate to what1

0 NAND 1 =1

1 NAND 1 =0

0 NAND 0 =1

The NAND gate computes the NAND operation: x↑y

The NOR gate computes the NOR operation:x↓y

The NAND gate outputs 0 if all inputs are _____ 1 The NOR gate outputs 1 if all inputs are _____0 The gate outputs 1 if all inputs are 0 and outputs _____ 0

1 NOR 1 =0

1 NOR 0 =0

0 NOR 0 =1

A two-input XOR gate (for "exclusive OR") outputs 1 if the input values differ. True or False True

1 XOR 0 =1

1 XOR 1 =0

0 XOR 0 =0

A two-input XNOR gate (for "exclusive NOR") outputs 1 if the input values are the same. True or False True

1 XNOR 0 =0

1 XNOR 1 =1

0 XNOR 0 =1

Which gate follows the same rules as Boolean multiplication?

AND Which gate follows the same rules as Boolean addition? OR What is the maximum length of a cycle in a graph? The amount of Vertices that connect.The proposition p ⊕ q is true if...Exactly one of the propositions p and q is true but not both Give DeMorgans Law for QUANTIFIED STATEMENTS (there are 2 laws) ¬∀xP(x) ≡ ∃x¬P(x) ¬∃xP(x) ≡ ∀x¬P(x)

Use DeMorgans Law to solve: ¬∃x P(x)∀x ¬P(x)

Use DeMorgans Law to solve: ¬∃x (P(x) ∨ Q(x)) ∀x (¬P(x) ∧ ¬Q(x))

Use DeMorgans Law to solve: ¬∀x (P(x) ∧ Q(x)) ∃x (¬P(x) ∨ ¬Q(x))

Is the variable y bound in the expression ∀xQ(x,y)? No

Is the following logical expression a proposition:

∀z∃yQ(x,y,z)?Why?No. X is not bound If the domain of a universal statement is small, it may be easiest to prove the statement by checking each element individually. A proof of this kind is called a _____ proof by exhaustion A _____ is an assignment of values to variables that shows that a universal statement is false counterexample When are XNOR gates equal to 0?When both inputs = 0 When both inputs = 1