Conditional Statements

Conditional Statements

–        If something, then something: p à q, p is called the hypothesis and q is called the conclusion

–        The only combination of circumstances in which a conditional sentence is false is when the hypothesis is true and the conclusion is false

–        A conditional statements is called vacuously true or true by default when its hypothesis is false

–        Among Ù, Ú, ~ and à operations, à has the lowest priority

–        Write truth table for: p Ù q à ~p

–        Show that (p Ú q) à r = (p à r) Ù (q à r)

–        Representation of à: p à q = ~p Ú q

–        Re-write using if-else: Either you get in class on time, or you risk missing some material

–        Negation of à: ~(p à q) = p Ù ~q

–        Write negation for: If it is raining, then I cannot go to the beach

–        Contrapositive p à q is another conditional statement ~q à ~p

–        A conditional statement is equivalent to its contrapositive

–        The converse of p à q is q à p

–        The inverse of p à q is ~p à ~q

–        Conditional statement and its converse are not equivalent

–        Conditional statement and its inverse are not equivalent

–        The converse and the inverse of a conditional statement are equivalent to each other

–        p only if q means ~q à ~p, or p à q

–        Biconditional of p and q means “p if and only if q” and is denoted as p « q

–        r is a sufficient condition for s means “if r then s”

–        r is a necessary condition for s means “if not r then not s”