1.5 Logic

In a worded sentence it declares a fact that is either true or false but not both.

It is a propositions that is made up of multiple propositions.

It just the opposite truth values of the proposition it is negating and mean "not" x

Conjunction mean joined and can be seen by two pints grounded between the two propositions or compounded propositions. 

This statement is only true when both its proposition components that are being conjoined are both true. They join in truth to make the statement true.

disjunction mean not joined and can be seen by only one ground contact point between the two propositions or compounded propositions. 

This statement is only true when both its proposition components that are being disjuncted are both false. They join in falseness to make the statement true.

• Name makes it very cleas that this statment is only true when there is only one of the propositions that is true and the other is false.
• Its like an or where one has to be tru but it is alse exclusive so the other part must be false if one is true for the statement to be true.

It is the combination of propositions and signs combining them.

A statements truth value depends on the T/F values in the propositions making up the statement and how they interact through the rules of how they change deepening on how you combine them.

• For "p => q"
• Means if p then q.
• Means p implies q
• Means p is hypothesis and q is conclusion.

The statement is only false when a true hypothesis leads to a false conclusion.

Converse: man har ett conditional statment och byter plats på de två propositionerna.

Inverse: man har ett conditional statment och negerar de två propositionerna i det.

Contrapositive: Man har ett conditional statment och både byerplats samt negerar de båda propositionerna.

• Also called bi implication
• For "p <=> q"
• Means "if and only if p then q.
• Means p is hypothesis and q is conclusion.

Only true when they have the same truth values, "bubble arrow means are they the same?" if to statment is true and if not statment is false.

The statement is only false when a true hypothesis leads to a false conclusion.

A statement that is true regardless of of what truth values you put in its propositions.

A statement that is false regardless of of what truth values you put in its propositions.

• Neither " always true or always false" = Contingency 
• So the truth value of the statement does actually change if toy change its truth values.

When a bi-conditional is always true.

• They tell us how to negate con-junctions and how to negate dis-junctions.
• It allows us to transform between two expressions because they have the same truth values, are a tautology.
• For a negating conjunction;
• -(p&q) = -pV-q
• For a negating dis-junction;
• -(pVq) = -p&-q

Is mean there is actually a combination of truth values in the propositions that make the satement true.

Is mean there is no combination of truth values in the propositions that make the satement true.

• A
• mathematical operation is called “idempotent” if it has the same result
• when applied two or more times in succession that it does when applied
• once. In Boolean algebra, both of the fundamental operators AND and OR
• are idempotent.