Assignment 1: Getting Started (This Week So Far) with Mathematical Notations

So far, I think I'm getting a pretty good grasp of the course material. (i.e, how to use venn diagrams to illustrate certain sets, implications, etc).

I DID find the usage of 'but' quite surprising, because I always used/interpreted 'but' with somewhat of a contradictory sense, but it is also a logically inclusive term (see? an use for 'but' as an addition to what I was saying before).

I also found the 'inclusive/exclusive or' in logic very interesting, because in real life, we use 'or' as a choice between options, and use 'and/or' for inclusive selection, but in logic it would just be 'or'. I think this is something that took a while for me to get used to in high school, when we were first introduced to notation for calculus.

ALSO in the spirit of beginning to tackle Assignment 1, I'm going to make a sufficiently comprehensive rundown of the symbols I'm gonna need to write this assignment (thanks Wikipedia):


 : implication, A ⇒ B means if A is true then B is also true; if A is false then nothing is said about B.

 : equivalence, A ⇔ B means A is true if B is true and A is false if B is false

 : logical negation, the statement ¬A is true if and only if A is false.

: logical conjunction, the statement A ∧ B is true if A and B are both true; else it is false.

: logical disjunction, the statement A ∨ B is true if A or B (or both) are true; if both are false, the statement is  
     false.

: universal quantification, ∀ x: P(x) means P(x) is true for all x.

: existential quantification, ∃ x: P(x) means there is at least one x such that P(x) is true.

, : set membership, a ∈ S means a is an element of the set S;^[6] a ∉ S means a is not an element of S.

, : subset, (subset) A ⊆ B means every element of A is also an element of B.^[7]

                      (proper subset) A ⊂ B means A ⊆ B but A ≠ B.

, : superset, A ⊇ B means every element of B is also an element of A.

                         A ⊃ B means A ⊇ B but A ≠ B.


: set union, A ∪ B means the set of those elements which are either in A, or in B, or in both

: set intersection, A ∩ B means the set that contains all those elements that A and B have in common.


Alright I think these are all we'll probably need for this assignment. Goodnight and good luck! 

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