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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*
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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'
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 a biconditional?
A biconditional is a statement wherein the truth of each item depends on the truth of the other.
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 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.
Lyndon B. Johnson The speech implies that America' prosperity?
must be brodened
