When is a conjunction statement false

Conjunction is a truth-functional connective similar to "and" in English and is represented in symbolic logic with the dot " ". Ordinary language definition of the dot: a connective forming compound propositions which are true only in the case when both of the propositions joined by it are true. One way of expressing this definition is by way of truth tables. Consider the following examples. There are four possible states of affairs which might have occurred with respect to John leaving and Carol arriving.

These cases can be listed as follows in what is called a truth table. It might be thought of in terms of a "minimum common logical meaning" to conjoined statements. Example p: Bill is travelling to Mexico q: Bill is travelling to Canada p or q gives us that Bill is travelling to Mexico or Bill is travelling to Canada.

A disjunction is true if at least one of the statements that form it is true. Video lesson We are given four statements p: cats have 4 legs true q: hens have 2 legs true r: cats lay egg false t: hens lay egg true Are the following compound statements true or false?

Search Math Playground All courses. All courses. Geometry Perpendicular and parallel Overview Angles, parallel lines and transversals. Geometry Similarity Overview Polygons Triangles. Let's look at some more examples of conjunction.

Solution: Since each statement given in this example represents an open sentence , the truth value of r s will depend on the value of variable x. But there are an infinite number of replacement values for x, so we cannot list all truth values for r s in a truth table.

We can, however, find the truth value of r s for given values of x as shown below. The conjunction r s is true. The conjunction r s is false. In the next example we are given the truth values of each statement. We are then asked to determine the truth values of the specified conjunctions. A conjunction is formed by combining two statements with the connector "and.

Summary: A conjunction is a compound statement formed by joining two statements with the connector "and. Directions: Read each question below. Select your answer by clicking on its button. If you make a mistake, choose a different button. By signing up, you agree to receive useful information and to our privacy policy. Shop Math Games. Skip to main content. Search form Search. Example 1: Given: p: Ann is on the softball team. Problem: What does p q represent?