Discrete Math exam review terms
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Statement - n
Ans✔
A statement (proposition) is a sentence that is either true or false, but not both.
Qs
Negation - n
Ans✔
A negation of a statement p is the statement "not p" or "it is not the case that p,"
and is denoted by ⌐p. A statement and its negation always have the opposite truth
value.
Qs
Conjunction - n
Ans✔
The conjunction of two statements p and q is the statement "p and q," and is
denoted by p ᴧ q. The conjunction p ᴧ q is true if both p and q are true and is false
otherwise.
Qs
Disjunction - n
Ans✔
The disjunction of two statements p and q is the statement "p or q," and is denoted
by p v q. The disjunction p v q is true if either of p and q are true or if both are true.
Qs
Conditional - n
,Ans✔
A statement of the form "if p, then q" where p and q are statements, is called a
conditional and is denoted by p -> q.
Qs
Forms of the conditional statement - n
Ans✔
The conditional, p→ q can be stated in any of the following ways:
If p, then q
q if p
p implies q
p only if q
p is sufficient for q
q is necessary for p
Qs
Tautology - n
Ans✔
A tautology is a statment that is always true no matter what truth values are
assigned to the statements appearing in it.
Qs
Fallacy(or Contradiction) - n
Ans✔
A fallacy(or Contradiction) is a statement that is always false.
Qs
Contingency - n
Ans✔
A statement that is sometimes false and sometimes true is called a contingency
, Qs
De Morgan's Law - n
Ans✔
For statements p and q,
⌐(p ᴧ q) ≡ ⌐p v ⌐q
⌐(p v q) ≡ ⌐p ᴧ ⌐q
Qs
Commutative Laws - n
Ans✔
pᴧq≡qᴧp
pvq≡qvp
Qs
Associative Laws - n
Ans✔
p ᴧ (q ᴧ r) ≡ (p ᴧ q) ᴧ r
p v (q v r) ≡ (p v q) v r
Qs
Distributive Laws - n
Ans✔
p ᴧ (q v r) ≡ (p ᴧ q) v (p ᴧ r)
p v (q ᴧ r) ≡ (p v q) ᴧ (p v r)
Qs
Impotent Laws - n
Ans✔
pᴧp≡p
completely explained 100%
guaranteed success.
Statement - n
Ans✔
A statement (proposition) is a sentence that is either true or false, but not both.
Qs
Negation - n
Ans✔
A negation of a statement p is the statement "not p" or "it is not the case that p,"
and is denoted by ⌐p. A statement and its negation always have the opposite truth
value.
Qs
Conjunction - n
Ans✔
The conjunction of two statements p and q is the statement "p and q," and is
denoted by p ᴧ q. The conjunction p ᴧ q is true if both p and q are true and is false
otherwise.
Qs
Disjunction - n
Ans✔
The disjunction of two statements p and q is the statement "p or q," and is denoted
by p v q. The disjunction p v q is true if either of p and q are true or if both are true.
Qs
Conditional - n
,Ans✔
A statement of the form "if p, then q" where p and q are statements, is called a
conditional and is denoted by p -> q.
Qs
Forms of the conditional statement - n
Ans✔
The conditional, p→ q can be stated in any of the following ways:
If p, then q
q if p
p implies q
p only if q
p is sufficient for q
q is necessary for p
Qs
Tautology - n
Ans✔
A tautology is a statment that is always true no matter what truth values are
assigned to the statements appearing in it.
Qs
Fallacy(or Contradiction) - n
Ans✔
A fallacy(or Contradiction) is a statement that is always false.
Qs
Contingency - n
Ans✔
A statement that is sometimes false and sometimes true is called a contingency
, Qs
De Morgan's Law - n
Ans✔
For statements p and q,
⌐(p ᴧ q) ≡ ⌐p v ⌐q
⌐(p v q) ≡ ⌐p ᴧ ⌐q
Qs
Commutative Laws - n
Ans✔
pᴧq≡qᴧp
pvq≡qvp
Qs
Associative Laws - n
Ans✔
p ᴧ (q ᴧ r) ≡ (p ᴧ q) ᴧ r
p v (q v r) ≡ (p v q) v r
Qs
Distributive Laws - n
Ans✔
p ᴧ (q v r) ≡ (p ᴧ q) v (p ᴧ r)
p v (q ᴧ r) ≡ (p v q) ᴧ (p v r)
Qs
Impotent Laws - n
Ans✔
pᴧp≡p
