what are two conditionals that form the statement below two numbers are reciprocals if and only if their product is 1
Conditional 1: If two numbers are reciprocals, then their product is 1.
Conditional 2: If the product of two numbers is 1, then they are reciprocals.
To form the statement "Two numbers are reciprocals if and only if their product is 1," we can formulate two conditionals:
Conditional 1: "If two numbers are reciprocals, then their product is 1."
Conditional 2: "If the product of two numbers is 1, then they are reciprocals."
These two conditionals together constitute the statement that you provided.
To understand the conditional statements that form the given statement "Two numbers are reciprocals if and only if their product is 1," we can break it down into two separate statements. Let's denote the two numbers as 'a' and 'b' and their product as 'ab'.
1. Conditional Statement 1:
"If two numbers are reciprocals, then their product is 1."
This statement asserts that if two numbers are reciprocals of each other (denoted as a and b), then their product (ab) equals 1.
2. Conditional Statement 2:
"If the product of two numbers is 1, then they are reciprocals."
This statement asserts that if the product of two numbers (ab) equals 1, then these numbers (a and b) are reciprocals of each other.
So, the two conditionals that form the given statement are:
1. If a and b are reciprocals, then ab = 1.
2. If ab = 1, then a and b are reciprocals.
To summarize:
Statement: "Two numbers are reciprocals if and only if their product is 1."
Conditional 1: If a and b are reciprocals, then ab = 1.
Conditional 2: If ab = 1, then a and b are reciprocals.