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IF-AND-ONLY IF statements have a double arrow symbol (⇔ ⇔) indicating both direction of the statement is true no matter which direction you start from. Eg: Former statement ⇔ ⇔ Latter statement. IF is the Backward direction (⇐ ⇐).
Apr 10, 2009 · For the purpose of diagramming your LSAT Logic Games we recommend the following: Note that IF AND ONLY IF is different than simply ONLY IF. Only If simply creates the reverse statement as if you used “IF”. So the statement “IF Mary is selected then Will is also selected” is the same as “Mary is selected ONLY IF Will is also selected ...
Apr 13, 2017 · You say it's the same as "only if". But it is not. "Only if", as you say, means "no guarantee he will yell if you fall". The first if provides just that guarantee. In other words, 3 is a combination of 1 and 2, and you simply failed to combine your correct reasoning for 1 and 2 into the correct reasoning for 3.
Aug 17, 2021 · The concept of a partition must be clearly understood before we proceed further. Definition 2.3.1: Partition. A partition of set A is a set of one or more nonempty subsets of A: A1, A2, A3, ⋯, such that every element of A is in exactly one set. Symbolically, A1 ∪ A2 ∪ A3 ∪ ⋯ = A A 1 ∪ A 2 ∪ A 3 ∪ ⋯ = A. If i ≠ j i ≠ j.
Lesson 7: Logic toolbox. Conditional reasoning and logical equivalence. If X, then Y | Sufficiency and necessity. The Logic of "If" vs. "Only if". A quick guide to conditional logic.
A 3 = A ∩ B 3. As it can be seen from the figure, A1 A 1, A2 A 2, and A3 A 3 form a partition of the set A, and thus by the third axiom of probability. P(A) = P(A1) + P(A2) + P(A3). Fig.1.24 - Law of total probability. Here is a proof of the law of total probability using probability axioms: Proof.
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In general, given two statement A and B, the statement "A if and only if B" is true precisely when both A and B are true or both A and B are false. [3] [4] In which case, A can be thought of as the logical substitute of B (and vice versa). [5] An "if and only if" statement is also called a necessary and sufficient condition. [6] [2] For example:
