Basic Forms of Statements  

The statements that a person might make are indefinitely large in number.  But certain basic forms occur frequently.  Consider the following two statements.

        Jack went up the hill and Jill went up the hill.
        Suzy loves dogs and Jim drinks too much.

Both of these have the form C: ________ and __________. What fills the blanks on both sides in both of these cases is a statement.  We call any statement of form C a conjunction.  Below are some especially useful basic forms of statements.  
 
Conjunction: a compound statement formed by inserting the word ‘and’ between two statements (note: other conjunction words besides ‘and’ can also be used, such as ‘but’, ‘yet’, ‘still’, ‘however’, ‘moreover’, ‘although’, ‘furthermore’, ‘also’, etc.).
Disjunction: a compound statement formed by inserting the word ‘or’ between two statements.
Conjuncts: the statements that are combined in a conjunction (ex. Mary has blue hair and Tom has purple hair); a conjunction is true only if both its conjuncts are true, but false otherwise.
Disjuncts: the statements that are combined in a disjunction (ex. Mark has a dog or Lisa has a cat); a disjunction is true unless both disjuncts are false.
Conditional statement: an “if p, then q” compound statement (ex. If I throw this ball into the air, it will come down); p is called the antecedent, and q is the consequent.  A conditional asserts that if its antecedent is true, its consequent is also true; any conditional with a true antecedent and a false consequent must be false.  For any other combination of true and false antecedents and consequents, the conditional statement is true.
Biconditional: a “p if and only if q” compound statement (ex. This ball will fall from the window if and only if it is dropped from the window); a biconditional is true when the truth value of the statements on both sides is the same, and false otherwise.

III. Validity and Invalidity, Soundness and Unsoundness