<Tr> <Td_colspan="2"> <Ul> <Li> </Li> <Li> </Li> <Li> </Li> </Ul> </Td> </Tr> <Ul> <Li> </Li> <Li> </Li> <Li> </Li> </Ul> <P> The circle on the left bounds all members of set A (\ displaystyle A), and the one on the right bounds all members of set B (\ displaystyle B). The red area describes all members for which the material conditional is true, and the white area describes all members for which it is false . The material conditional differs significantly from a natural language's "if...then ..." statement . It is only false when both the antecedent A (\ displaystyle A) is true and the consequent B (\ displaystyle B) is false .)) </P> <P> The material conditional (also known as material implication, material consequence, or simply implication, implies, or conditional) is a logical connective (or a binary operator) that is often symbolized by a forward arrow "→". The material conditional is used to form statements of the form p → q (termed a conditional statement) which is read as "if p then q". Unlike the English construction "if...then ...", the material conditional statement p → q does not specify a causal relationship between p and q . It is merely to be understood to mean "if p is true, then q is also true" such that the statement p → q is false only when p is true and q is false . The material conditional only states that q is true when (but not necessarily only when) p is true, and makes no claim that p causes q . </P>

In which cases is a conditional statement of the form if a then b false
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