D420 Discrete Math: Logic Questions and Correct Answers 100%!! With Diagrams for EASY UNDERSTANDING
proposition
a statement that is either true or false
^
and
D420 Discrete Math: Logic Questions and
Correct Answers 100%
With diagrams for illustrations
proposition
a statement that is either true or false
A
^
and
VI
v
TU
IS
or
OM
¬
NA
negation
→
conditional operation, "if p, then q"
JP
Equivalent English expressions that mean "if p, then q"
If p, q
q, if p
, p implies q
p only if q
p is sufficient for q
q is necessary for p
in a conditional proposition "→" p is the _______ and q is the __________
p is the hypothesis and q is the conclusion
The converse is the opposite of the conditional statement
For example, the converse of p → q (if p then q) is q → p (if q then p). If p → q is true, it
A
does NOT guarantee that q → p is true
VI
The inverse is the negation of the conditional statement
For example, the inverse of p → q (if p then q) is ¬p → ¬q (if not p then not q). If p → q
is true, it does NOT guarantee that ¬p → ¬q is true
TU
The contrapositive is the opposite and negative of the conditional statement
For example, the contrapositive of p → q (if p then q) is ¬q → ¬p (if not q then not p). If
p → q is true, it DOES guarantee that ¬q → ¬p is true
IS
biconditional operation
is read "p is necessary and sufficient for q" or "if p then q, and conversely" or "p if and
OM
only if q"
NA
Logical equivalence p ≡ q
Two compound propositions are logically equivalent if they have the same truth value.
JP
That is, the truth value in the final column in a truth table is the same for both compound
propositions
tautology
If the compound propositions is always true. For example, p∨¬p.
contradiction
if the compound proposition is always false. For example, p∧¬p.
De Morgan's Law
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