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LOGIC MAIN PAGE

LOGICAL OPERATORS

Sample sentences
AND operator
IF/THEN operator
NOT operator
OR operator
XOR operator

RULES OF LOGIC

Chain Rule
Conjunctive Addition
Contrapositive
DeMorgan's Law
Disjunctive Addition
Disjunctive Inference
Disjunctive Infer. (XOR)
Double Negation
Modus Ponens
Modus Tollens
Mutual Exclusion
Simplification

VALIDITY PROOFS

2-step
3-step
4-step
5-step or more
Bad Argument

Conjunctive Addition

Conjunctive Addition is a rule of inference pertaining to the AND operator.

Conjunctive Addition means that any two true statements can be joined to form a conjunction.

If statement p and statement q are given, then their conjunction p ^ q follows logically. In an argument any two statements may be joined by conjunction. The order of the conjuncts is unimportant because p ^ q is equivalent to q ^ p.

Imagine we are given two separate statements: 1) The triangle has a right angle, and 2) The base angles are equal. We can join these two statements by saying, "The triangle has a right angle, and the base angles are equal." Formally, we would write:

p: "The triangle has a right angle."
q: "The base angles are equal."
----------
p ^ q: "The triangle has a right angle, and the base angles are equal."

The given p and q statements are above the line of dashes, and the new expression p ^ q formed by applying Conjunctive Addition is below the line.

 

Other examples of Conjunctive Addition

~A: "It's not raining."
B: "The sun is shining brightly."
----------
~A ^ B: "It's not raining, and the sun is shining brightly."


X: "The grass is green."
Y: "The sky is blue."
----------
Y ^ X: "The sky is blue and the grass is green."

 

Links to Relevant Problems

These are links to validity proof problems whose solutions contain Conjunctive Addition.

2-step problem
4-step problem
5-step problem