Explain the follwoing terms with examples:?

Question

Explain the follwoing terms with examples:

a. Conjuntion

b. Disjuntion

c. Negation

d. Implicational

e. Bi-conditional

Answer 1

a. Conjuntion
I went to the beach AND I saw Sam.

b. Disjuntion
I went to the beach OR I saw Sam. (either/both)

c. Negation
I did NOT go to the beach.

d. Implicational
IF I went to the beach THEN I would see Sam

e. Bi-conditional
I would go to the beach IF AND ONLY IF I saw Sam.

Answer 2

a) A conjunction is simply, an AND, or any homonym of and. I'm not sure if you want examples of symbolic logic, or examples with real sentences.

A and B is a conjunction. As long as A and B are true statements, A and B are both true. If one of A or B is false, then the statement is false overall.

Example:

The world is round, and water is liquid.
This is a true statement, because the first part is true and the second part is true.

Birds have feathers and water is dry.
This is a false statement, because the second part is clearly false.


b) A disjunction is an OR.

A or B is a disjunction.

As long as one of A or B is true, the whole thing is true. It is only if both of A and B is false that the whole statement is false.

Christmas is on December 25 or bread is made from flour.
(That is a true statement).

Snow is cold or fire is cold.
(This is a true statement, even though there's a false statement in there)

Dogs meow and cats bark.
(This is false).

c. Negations apply to only one sentence, and it means "It is not the case that". In symbolic logic, it is represented as

NOT (A), and, as you can see, only applies to one term. When applied to a true statement, it makes the entire sentence false. When applied to a false statement, it makes the entire sentence true.

Examples:

It is not the case that fish breathe air.
{This is a true statement}

It is not the case that fish swim.
{This is a false statement}.

d. Implicationals are IF-THENs.
IF A, then B.

e. Biconditionals are IF AND ONLY IF statements.

A if and only if B means
If A then B and
if B then A

Answer 3

a) Conjunction is the logical AND.

A conjunction of two sentences is true only if both the sentences it connects are true.

Bush is the President AND I am a girl. (False, because I'm a guy.)

b) Disjunction is the logical OR.

A disjunction of two sentences is true if either of the sentences it connects are true.

Bush is the president OR I am a girl. (True, because Bush is the president; doesn't matter that I'm not a girl.)

c) Negation is the logical NOT.

A negation reverses the truth value of the sentence it affects. If it was true before, it becomes false; if false before, it becomes true.

I am NOT a girl. (true, "I am a girl" is false.)

d) Implication is the logical IF, THEN.

An implication is false only if the first part (the hypothesis) is true, and the second part is false.

IF I am a girl, THEN Bush is not the president. (This is true, even though I'm not a girl and Bush is the president. It's always true if the first part is false.)

e) Biconditional is the logical IF AND ONLY IF.

A biconditional is true if both parts are true or both parts are false; otherwise it is false.

Bush is not the president if and only if I am a girl. (True, because both parts are false.)