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


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


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