Not necessarily. It will all depend on the statements A and B.
a is a subset of b
if a is bigger than b and b is bigger than c a must be bigger than c... Transitivity
An example of a conditional statement is: If I throw this ball into the air, it will come down.In "if A then B", A is the antecedent, and B is the consequent.
a < b → a - a < b - a → 0 < b - a → 0 - b < b - a - b → -b < -a → if a < b then -b < -a which can also be expressed as -a > -b
novanet; they felt that paliament and the crown must be obeyed as the legitament govenment of the empire
if a is true, then b must be true
a is a subset of b
not b not a its contrapositive
This describes one kind of statement that can appear in a logical syllogism or argument. If a given argument A is true, then it follows that argument B must be true. It does not automatically follow that if B is true, then A must be true.'All living humans are breathing animals' is true. [If you are a living human (A) you breathe (B).'All breathing animals are therefore human' is not true. [If you breathe (B) you are a living human (A).
This describes one kind of statement that can appear in a logical syllogism or argument. If a given argument A is true, then it follows that argument B must be true. It does not automatically follow that if B is true, then A must be true.'All living humans are breathing animals' is true. [If you are a living human (A) you breathe (B).'All breathing animals are therefore human' is not true. [If you breathe (B) you are a living human (A).
if a is bigger than b and b is bigger than c a must be bigger than c... Transitivity
The law of detachment says that in cases where A implies B, if A is true, B must also be true. For example, if A says that this is a shark, and B says that it lives in the ocean, we can conclude that if A is true, B is also true, and it lives in the ocean.
An example of a conditional statement is: If I throw this ball into the air, it will come down.In "if A then B", A is the antecedent, and B is the consequent.
True
No
a < b → a - a < b - a → 0 < b - a → 0 - b < b - a - b → -b < -a → if a < b then -b < -a which can also be expressed as -a > -b
It is a logical conditional statement which states that if some condition, a, is satisfied then another condition, b, must be satisfied. If a is not satisfied then we can say nothing about b.An equivalent statement, in a non-conditional form, is that~b or a must be TRUE, where ~b denotes not b.