MAT 167 Logical Operators
A ? is a statement that cancels out or denies another statement or action.
"I didn't kill the butler". - ANS-∼, ¬ (Negation)
A ? is a statement formed by adding two statements with the connector AND.
"pie is tasty" and "cake is yummy" is the statement "pie is tasty, and cake is yummy." - ANS-∧,
& (Conjunction)
A ? is a compound statement formed by joining two statements with the connector OR.
"Gujarat is a state of India or Ahmedabad is in Maharashtra." - ANS-∨ (Disjunction)
A relationship between two propositions in which the second is a logical consequence of the
first.
A = The sky is overcast. B = The sun is not visible. Using the above sentences as examples, we
can say that if the sun is visible, then the sky is not overcast. - ANS-→ (Implication)
A relation between two propositions that is true only when both propositions are simultaneously
true or false.
? statements: "I will eat lunch if and only if my mood improves." "My mood will improve if and
only if I eat lunch." - ANS-↔ (Bi-Conditional)
Two expressions are ? provided that they have the same truth value for all possible
combinations of truth values for all variables appearing in the two expressions.
"If Ryan gets a pay raise, then he will take Allison to dinner." - ANS-≡ (Logical Equivalent)
A ? is a statement that cancels out or denies another statement or action.
"I didn't kill the butler". - ANS-∼, ¬ (Negation)
A ? is a statement formed by adding two statements with the connector AND.
"pie is tasty" and "cake is yummy" is the statement "pie is tasty, and cake is yummy." - ANS-∧,
& (Conjunction)
A ? is a compound statement formed by joining two statements with the connector OR.
"Gujarat is a state of India or Ahmedabad is in Maharashtra." - ANS-∨ (Disjunction)
A relationship between two propositions in which the second is a logical consequence of the
first.
A = The sky is overcast. B = The sun is not visible. Using the above sentences as examples, we
can say that if the sun is visible, then the sky is not overcast. - ANS-→ (Implication)
A relation between two propositions that is true only when both propositions are simultaneously
true or false.
? statements: "I will eat lunch if and only if my mood improves." "My mood will improve if and
only if I eat lunch." - ANS-↔ (Bi-Conditional)
Two expressions are ? provided that they have the same truth value for all possible
combinations of truth values for all variables appearing in the two expressions.
"If Ryan gets a pay raise, then he will take Allison to dinner." - ANS-≡ (Logical Equivalent)
