# Week 4 Logic

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Question

What is Modus Ponens rule?
if this then that or " if X then Y" is true and "X" is true => so "Y " must be true

What is a proposition?
A declarative statement that is either true or false but not both.

what is => mean?
implies; if ... then

what are the propositional variables?
Each propositional variable has one of two truth values: true or false

what is a compound statment?
A compound statement is a sentence that consists of two or more statements separated by logical connectors.

what is the negation (not) connective symbol?
¬

what is the conjunction (and) connective symbol?
^

What is the disjunction (or) connective symbol)
V

what is the connective symbol for implication (if-then)
-> or =>

What is the biconditional (if and only if) connective symbol?
<=> or <->

what order are connective symbols considered in?
1) brackets, 2) negation, 3) conjunction dissjunctive, 4) implication bicnditional

what is a tautology statement?
true for all possible values of its propositional variables is called a tautolog

false for all possible values of its propositional variables is called a contradiction

what is the symbol for logical equivalence?

define logical equivalent
Two statements are said to be logically equivalent,≡, if they have identical truth values for each possible value of their statement variables. (Corresponds to = with numbers)

define commutative law
refers to moving stuff around. For addition, the rule is "a + b = b + a"; in numbers, this means 2 + 3 = 3 + 2. For multiplication, the rule is "ab = ba"; in numbers, this means 2×3 = 3×2.

define distributive law
"multiplication distributes over addition". Formally, they write this property as "a(b + c) = ab + ac". In numbers, this means, for example, that 2(3 + 4) = 2×3 + 2×4.

define de morgans law
The complement of the union of two sets is equal to the intersection of their complements and the complement of the intersection of two sets is equal to the union of their complements.

conditional statement consists of two parts, a hypothesis the “if” clause and conclusion the “then” clause. For instance “If it rains, then they cancel school.” "It rains" is the hypothesis. "They cancel school" is the conclusion. what is the converse?
To form the converse of the conditional statement, interchange the hypothesis and the conclusion. The converse of "If it rains, then they cancel school" is "If they cancel school, then it rains."

conditional statement consists of two parts, a hypothesis the “if” clause and a conclusion the “then” clause. For instance, “If it rains, then they cancel school.” "It rains" is the hypothesis. "They cancel school" is the conclusion. what is the inverse
To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion. The inverse of “If it rains, then they cancel school” is “If it does not rain, then they do not cancel school.”

CHANGE ME
To form the contrapositive of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement. The contrapositive of "If it rains, then they cancel school" is "If they do not cancel school, then it does not rain

define sufficient condition
a condition that must be satisfied for a statement to be true and without which the statement cannot be true

define necessary condition
a condition that must be present for an event to occur. A sufficient condition is a condition(s) that will produce the event. A necessary condition must be there, but it alone does not provide sufficient cause for the occurrence of the event.