Formal Logic: if and only if Flashcards
What is the logical operator called for if and only if?
What symbol do we use to represent it?
What is it often written as?
2 x Example sentences
Logical operator is called the ‘biconditional’
We use
Written as iff
You may have pudding you’ve finished your greens
Students pass logic they study properly for the exam.
How do we make A iff B?
When is A iff B true?
To make ‘A if and only if B’ true, we need both ‘A if B’ and ‘A only if B’ to be true. So we combine the two truth tables.
A if and only B is true if A and B have the same truth value, both must be true or both must be false.
Truth table for A B
Difference between Necessary and sufficient conditions with examples
A necessary condition for X is something without which X cannot be. (must be present for an event to occur)
Eg being a mammal is a necessary condition for being a horse/ must have ingredients to bake a cake. (However, it is not sufficient, cats and dogs are also mammals and you may not have an oven or time to bake a cake)
A sufficient condition for X is something which suffices for X to be. (This being true will bring about the event)
Eg.Being born in the US is a sufficient condition for being a US citizen (but it is not necessary: you might be born elsewhere in the world to American parents).
What is a necessary and sufficient condition? with examples
It is a necessary and sufficient clause combined
Eg. being a valid argument with true premises is a necessary and sufficient condition for being a sound argument.
An argument is sound iff it is a valid argument and its premises are true.
Eg. being a male sibling is a necessary and sufficient condition for being a brother
Explain necessary and sufficient in logic with examples
A -> B implies that B is necessary for A
(Eg if something is a horse, then it is a mammal)
A -> B implies that A is sufficient for B
(If someone is born in the US, then they are a US citizen)
A B implies that A is necessary and sufficient for B and B is necessary and sufficient for A.
