A replacement for a variable that results in a true sentence is often referred to as a "satisfying assignment." For example, in the logical statement "x > 5," replacing the variable x with 6 makes the sentence true, as 6 is indeed greater than 5. This principle is foundational in logic and mathematics, where finding such replacements can validate propositions or equations.
a "solution"
A replacement for the variable in an open sentence is called a "substitution." In mathematical terms, it refers to the process of replacing the variable with a specific value or expression to evaluate the truth of the statement. For example, in the open sentence "x + 2 = 5," substituting x with 3 would allow you to check if the equation is true or false.
To replace a variable with a value that results in a true sentence, first identify the condition or statement in which the variable is used. Substitute the variable with different potential values and evaluate the resulting sentence for truthfulness. Continue testing values until you find one that satisfies the condition, making the entire statement true. This process often involves logical reasoning or basic algebra if the statement is mathematical in nature.
Answer 1 == In an open sentence (an equation or inequality with a variable in it), when a number replacing the variable makes the sentence true, then it is a solution.
TRUE!
A Solution
a "solution"
That's the "solution" to the equation described by the sentence.
That's the "solution" to the equation described by the sentence.
Solution.
Answer 1 == In an open sentence (an equation or inequality with a variable in it), when a number replacing the variable makes the sentence true, then it is a solution.
Because it is neither true or false until the variable is replaced with a specific value making the sentence true or false.
TRUE!
Oh, what a happy little question you have there! When we replace a variable with a value in an equation or sentence and it makes the sentence true, we're finding a solution that works perfectly. It's like adding a touch of color to a blank canvas, bringing harmony and balance to the mathematical world. Just remember, there are infinite possibilities waiting to be discovered!
It is an identity.
True
true