PROPERTIES OF PROPOSITIONAL LOGIC
properties of propositional logic
Equivalence
Contraposition
Satisfiability
Entailment
Implication
relationship between two propositions A->B
e.g : sentences A and B A=The sky is overcast B=The sun is not visible -which the second is a logical consequences of the first
immediate reference in which a proposition is inferred from another. e.g. if it is raining, then the grass is wet ->TRUE
Contraposition : if the grass is not wet, then it is not raining ->TRUE
statement p and q are said to be logically equivalent if they have the same truth value
e.g. P->Q is logically equivalent to -P v Q
if a number is a multiple of 4 then it is even is equivalent to a number is not a multiple of 4 or (else) it is even
Tautology
Either the ball is green or the ball is not green is always true regardlwss of the color of the ball
Contradictions
Every S is P and some S is not P
A formula is calles satisfiability if
it is true for at least one interpretation
Logically valid or simply valid if it is true for all interpretations. True formulas are also called tautologies
Unsatisfiable if it is not true for any interpretation. Every interpretation that satisfies a formula is called a model of the formula
the relationship between statement that hold true when one statement logically follows from one or more statement
e.g. If two sentences x and y are related by entailment
If x is true, then y must also be true; if y is false, then x must also be false
sound
an argument is sound if it is both valid in form and its premises are true
eg.
WAN NUR AFIQAH BINTI ZULKEFLI (D20191089434)