Write the component statements of the following compound statement and check whether compound statement is true or false . Two lines intersect at a point or they are parallel"

Answer

To solve the given question step by step, we will break down the compound statement into its component statements and then evaluate the truth of the compound statement.

### Step 1: Identify the Component Statements
The compound statement given is: "Two lines intersect at a point or they are parallel."

We can define the component statements as follows:
- Let \( p \): "Two lines intersect at a point."
- Let \( q \): "Two lines are parallel."

### Step 2: Write the Compound Statement
The compound statement can be expressed using logical operators. Since the statement uses "or," we can represent it as:
- Compound Statement: \( p \lor q \) (where \( \lor \) denotes logical OR)

### Step 3: Analyze the Truth of the Component Statements
Now we need to check the truth values of the component statements:
- Statement \( p \) (Two lines intersect at a point) can be true if the lines actually intersect.
- Statement \( q \) (Two lines are parallel) can be true if the lines do not intersect and are parallel.

### Step 4: Determine the Truth of the Compound Statement
According to geometry, two lines in a plane can either:
1. Intersect at a point (making \( p \) true).
2. Be parallel (making \( q \) true).

Since at least one of the component statements \( p \) or \( q \) must be true for the compound statement \( p \lor q \) to be true, we conclude that the compound statement is true.

### Final Conclusion
The compound statement "Two lines intersect at a point or they are parallel" is **true**.