Two types of connectives that you often see in a compound statement are conjunctions and disjunctions, represented by ∧ and ∨, respectively.
It’s important to know the difference between these two connectives.
Identifying a conjunction
The conjunction, p ∧ q, puts the word and between two statements to create a compound statement.Consider the following statements:
(1) Chicago is a city in Illinois.
(2) Red is a color in the American flag.
(3) 7 + 3 = 11.
(4) San Francisco is a city in Florida.
Statements (1) and (2) are true, and Statements (3) and (4) are false.
Next, you construct a truth table for the conjunction p ^ q.
![FNTMATH_0203](https://www.dummies.com/wp-content/uploads/FNTMATH_0203.jpg)
Referring to the first line of Ts and Fs in the table, when both statements are true, their conjunction p ^ q is true. For example, using Statements (1) and (2), the conjunction reads: “Chicago is a city in Illinois, and red is a color in the American flag.”
The second line of Ts and Fs says that when the first statement is true and the second is false, their conjunction p ^ q is false. Using Statements (1) and (3), the conjunction reads: “Chicago is a city in Illinois, and .”
In the third line, when the first statement is false and the second statement is true, their conjunction p ^ q is false. Using Statements (4) and (2), the conjunction reads: “San Francisco is a city in Florida, and red is a color in the American flag.”
And, finally, when both statements are false, their conjunction is false. Using Statements (3) and (4), the conjunction reads: “7 + 3 = 11, and San Francisco is a city in Florida.”
Basically, what you see here is that for a conjunction to be true, both of the component statements have to be true.
Identifying a disjunction
The disjunction, p ∨ q, uses the word or to create a compound statement.The truth table for the disjunction is shown here:
![FNTMATH_0205](https://www.dummies.com/wp-content/uploads/FNTMATH_0205.jpg)
For a disjunction to be true, only one of the component statements needs to be true. Consider the following compound statements representing the four rows.
![FNTMATH_0206](https://www.dummies.com/wp-content/uploads/FNTMATH_0206.jpg)
Both are true; the compound statement is true.
TF: “It rains in Hawaii, or all cows have seven legs.” The first statement is true, so the compound statement is true.
![FNTMATH_0207](https://www.dummies.com/wp-content/uploads/FNTMATH_0207.jpg)
The second statement is true, so the compound statement is true.
FF: “All cows have seven legs, or pigs can fly.” Both statements are false, so the compound statement is false.