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YES! If a->b is true then ~b->~a is also true. Changing a->b to ~b->~a is called taking the contrapositive where "->" means implication and "~" means "not."
For example, if A = Chevrolet Corvette and B = Automobile then A->B and B doesn't necessarily imply A. But if it's not an automobile, it's certainly not a corvette. So ~B->~A follows from A->B.
*The other answer misunderstood the question and reported correctly that a->b doesn't not mean that b->a; however, the question asked was about the statement ~b->~a, which is true given a->b.
NO
A=Chevrolet Corvett
B=Automobile
A = B
But
B<>A
All As are Bs
BUT
Not All Bs are As*
What else can I help you with?
Which property is illustrated by the following statementIf AHAX= A RIG, then A RIG= A HAX?
Answer: The property that is illustrated is: Symmetric property. Step-by-step explanation: Reflexive property-- The reflexive property states that: a implies b Symmetric Property-- it states that: if a implies b . then b implies a Transitive property-- if a implies b and b implies c then c implies a Distributive Property-- It states that: a(b+c)=ab+ac If HAX implies RIG then RIG implies HAX is a symmetric property.
What is the converse of if a shape is a rectangle then it is a parallelogram?
~(A => B) is ~B => ~A That is to say, the converse of "A implies B" is "the converse of B implies the converse of A". In this case: If a shape is not a parallelogram then it is not a rectangle.
What is a contrapositive in math?
Contrapositives are an idea in logic which is very useful in math.We say that A implies B if whenever Statement A is true then we know that statement B is also true.So, Say that A implies B, written:A -> BThe contrapositive of this statement is:Not-B -> Not-ARemember "A implies B" means that B must be true if A is true, so if we know that B is falce, we can deduce that A couldn't be true, so it must be falce.With truth tables it can easily be shown that"A -> B" IF AND ONLY IF "Not-B -> Not-A"So when using the contrapositive, no information is lost.In math, this is often used in proofs when, while trying to demonstrate that A implies B, it is easier to show that Not-B implies Not-A and hence that A implies B.
What is an arrow with two lines in mathematics?
== == It means 'implies'. So A --> B means 'if A is true then B is true' or 'A implies B'
What is a biconditional?
A biconditional is a statement wherein the truth of each item depends on the truth of the other.
When do you know if the range of numbers includes the number?
The answer depends on the way in which the range is given. a < x < b or x Î (a, b) implies that both bounds are not included.a < x ≤ b or x Î (a, b] implies that the lower bound is not included but the upper one is.a ≤ x < b or x Î [a, b) implies that the lower bound is included but the upper one is not.a ≤ x ≤ b or x Î [a, b] implies that both bounds are included.
What is the relationship between a and b if LCM of ab equals a?
It implies b is a factor of a.
What is the principal of simplification A implies that B implies A?
The principle of simplification in logic states that if a statement A implies B, then A can be considered sufficient on its own to support the truth of B. This means that knowing A is true allows us to deduce that B must also be true. The statement can be expressed as "If A, then B" (A → B), and the idea is that the truth of A leads directly to the truth of B. Thus, in a logical framework, A serves as a premise from which B logically follows.
What is the greater of two numbers whose product is 900 if sum of the two numbers exceeds their difference by 30?
Suppose the two numbers are A and B, with A > B.Then A + B = A - B + 302B = 30 and so B = 15Then AB = 900 implies A = 900/B = 900/15 = 60.Suppose the two numbers are A and B, with A > B.Then A + B = A - B + 302B = 30 and so B = 15Then AB = 900 implies A = 900/B = 900/15 = 60.Suppose the two numbers are A and B, with A > B.Then A + B = A - B + 302B = 30 and so B = 15Then AB = 900 implies A = 900/B = 900/15 = 60.Suppose the two numbers are A and B, with A > B.Then A + B = A - B + 302B = 30 and so B = 15Then AB = 900 implies A = 900/B = 900/15 = 60.
What is an example of a reflective relation?
A reflective relation is one where the relation holding between A and B implies that the relation also holds between B and A 'sibling' is a reflective relation. A is B's sibling implies that B is A's sibling. In contrast, 'sister' is not reflective, A is B's sister does not imply that B is A's sister (for B might be male).
What is the contrapositive of the statement below?
The concept of contrapositive comes from here. A implies B is equivalent to not B implies not A. Prove by contrapositive means instead of proving condition A leads to B, show that if B fails also cause A to fail.
What did Lyndon B. Johnson The speech implies that America's prosperity?
must be retained There was a sense of national decline.
