College first year BSc mathematics notes

BSc 1st Year Mathematics Notes



1. Sets and Relations


Definition of Set: A set is a well-defined collection of distinct objects.

Example:

- Set of vowels: A = {a, e, i, o, u}

- Set of natural numbers: N = {1, 2, 3, 4, ...}



Types of Sets:

1. Finite Set: A set with a limited number of elements.

2. Infinite Set: A set with an unlimited number of elements.

3. Empty (Null) Set: A set with no elements (phi or {}).

4. Equal Sets: Two sets are equal if they contain the same elements.

5. Subset: A is a subset of B if every element of A is also in B.

6. Power Set: The set of all subsets of a set A.

7. Universal Set: The set that contains all possible elements under consideration.



Operations on Sets:

1. Union of Sets: A union B = {x : x in A or x in B}

2. Intersection of Sets: A intersection B = {x : x in A and x in B}

3. Difference of Sets: A - B = {x : x in A and x not in B}

4. Complement of a Set: A' = U - A



De Morgan's Laws:

1. (A union B)' = A' intersection B'

2. (A intersection B)' = A' union B'

2. Matrices and Determinants


Definition of a Matrix: A matrix is a rectangular array of numbers arranged in rows and columns.



Types of Matrices: