# Geometry is fun or ducks do not like water. Is this conjunction, disjunction, negation, or conditional?

Nov 22, 2016

This is a disjunction:

Geometry is fun $\text{ }$ or $\text{ }$ ducks do not like water.

#### Explanation:

This is a disjunction of two clauses: "geometry is fun" and "ducks do not like water". The central connective word is "or".

It is approximately logically equivalent to the conditional statement:

If ducks like water then geometry is fun.

We can break it down into parts as follows:

• Let $G$ be the statement "geometry is fun".

• Let $D$ be the statement "ducks like water".

Then the given statement can be represented symbolically as:

$G \vee \neg D \text{ }$ "G or not D"

The statement "If ducks like water then geometry is fun." would be represented as:

$D \to G \text{ }$ "D implies G"

These two statements are equivalent in Boolean logic.

We can draw a Venn diagram looking like this:

The left hand circle represents the proposition "geometry is fun" and the right hand circle the proposition "ducks like water".

The shaded region corresponds to both the statements:

$G \vee \neg D \text{ }$ "Geometry is fun or ducks do not like water."

$D \to G \text{ }$ "If ducks like water then geometry is fun."

However, I think that it is important to note that natural language and meaning are more subtle than Boolean logic. So it would be inaccurate to classify the given statement as a conditional.