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The sum rule is given by P(A + B) = P(A) + P(B). Explain that A and B are each events that could occur, but cannot occur at the same time.

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The product rule is P( E​F) = P(E)​P(F) where E and F are events that are independent.

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A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

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The transpose of a matrix is simply a flipped version of the original matrix. We can transpose a matrix by switching its rows with its columns.

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A proposition is simply a statement with a definite meaning, having a truth value that’s either true or false

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When the order does matter it is a Permutation.

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A matrix can only be added or subtracted from another matrix if the two matrices have the same dimensions.

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If A is an m × n matrix and B is an n × p matrix, the matrix product C = AB is defined to be the m × p matrix

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The identity matrix is a matrix in which the diagonal entries are 1, and all other entries are zero.

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The determinant is a scalar value that is a function of the entries of a square matrix.

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The inverse of matrix is another matrix, which on multiplication with the given matrix gives the multiplicative identity. For a matrix A, its inverse is A-1, and A.A-1 = I.

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A set is a collection of objects, things or symbols which are clearly defined.

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A linear equation is an equation that is written for two different variables. This equation will be a linear combination of these two variables, and a constant can be present.

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A set can be defined by describing the contents, or by listing the elements of the set, enclosed in curly brackets.

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Finite sets are sets having a finite or countable number of elements.
Infinite set can be understood as a set that is not finite. It is not possible to count the elements of an infinite set.

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The empty set is a set that has no elements. It is usually denoted by some variant of zero with a line through it, for example, ∅ and can always be represented as {}.

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A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items.

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A universal set (usually denoted by U) is a set that has elements of all the related sets, without any repetition of elements.

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A set a is a subset of another set b if all elements of set a are elements of set b. In other words, set a is contained inside set b. The subset relationship is

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The complement of set A, denoted by A’ , is the set of all elements in the universal set that are not in A. It is denoted by A’

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Difference of set A and B means all elements of set A which are not in B.

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The power set is a set that includes all the subsets including the empty set and the original set itself.

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A system of linear equations is usually a set of two linear equations with two variables.

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Solving Systems of Linear Equations Using Matrices

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Solving Systems of Linear Equations Using Matrices

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First, we need to find the inverse of the A matrix
Then multiply the inverse of A by B
And we are done.

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A compound statement, that is always true regardless of the truth value of the individual statements is defined to be a tautology.

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Logically equivalent statements are if statements have the same truth value in every model.

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When the order doesn't matter, it is a Combination.

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The events have to be independent

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The probability that either one of 2 different events will occur is the sum of their separate probabilities.

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The chance of an event not happening is 1 minus the chance of it happening.

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More complicated situations involve combining the AND and OR rules.

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Knowing that an event B occurred might affect the probability that another event A also occurred.