Write two conditional statements that make up each bioconditinal.
1. A whole number is multiple of 5 and only if its last digit is ethier a 0 or a 5.
2. Two lines are perpendicular if and only if they intersect to form four right angles.
3. You live in Texas if and only if you live in the largest state in the contiguous United States.
1. To form a biconditional statement for the relationship between whole numbers and being a multiple of 5, we can express it in two conditional statements:
- If a whole number is a multiple of 5, then its last digit is either 0 or 5.
- If the last digit of a whole number is 0 or 5, then it is a multiple of 5.
In symbolic form:
- A: The whole number is a multiple of 5
- B: The last digit of the whole number is 0 or 5
The biconditional statement would be: A ↔️ B
So, the two conditional statements that form this biconditional statement are:
- A → B (If the whole number is a multiple of 5, then its last digit is 0 or 5)
- B → A (If the last digit of the whole number is 0 or 5, then it is a multiple of 5)
2. For the relationship between two lines being perpendicular and forming four right angles, we can have the following conditional statements:
- If two lines are perpendicular, then they intersect to form four right angles.
- If two lines intersect to form four right angles, then they are perpendicular.
In symbolic form:
- A: Two lines are perpendicular.
- B: They intersect to form four right angles.
The biconditional statement would be: A ↔️ B
The two conditional statements that form the biconditional statement are:
- A → B (If two lines are perpendicular, then they intersect to form four right angles)
- B → A (If two lines intersect to form four right angles, then they are perpendicular)
3. For the relationship between living in Texas and living in the largest state in the contiguous United States, we can establish the following conditional statements:
- If you live in Texas, then you live in the largest state in the contiguous United States.
- If you live in the largest state in the contiguous United States, then you live in Texas.
In symbolic form:
- A: You live in Texas.
- B: You live in the largest state in the contiguous United States.
The biconditional statement would be: A ↔️ B
The two conditional statements that form the biconditional statement are:
- A → B (If you live in Texas, then you live in the largest state in the contiguous United States)
- B → A (If you live in the largest state in the contiguous United States, then you live in Texas)