{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "[//]: # (Long-Title: Set Union Operation and Venn Diagram for Set Union)\n", "\n", "[//]: # (Short-Title: Set Union Operation)\n", "\n", "[//]: # (Keyword: Union of Sets)\n", "\n", "[//]: # (Keyword: Venn Diagram for Union of Sets)\n", "\n", "[//]: # (Keyword: Null Set)\n", "\n", "[//]: # (Keyword: Empty Set)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Set Union Operation " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The union of two sets is a set which contains elements from both the sets.
\n", "The union of two sets A and B is denoted by $A \\cup B$.

\n", "Example:
\n", "Set A = {1,2,3,4} and B = {3,4,5,6}
\n", "$A \\cup B$ = {1,2,3,4,5,6}

\n", "Note: By definition, sets do not contain duplicates. If an element appears in both sets, we include it only once in the result.

\n", "More formally,
\n", "$A \\cup B = \\left \\{x| x \\in A \\; or \\; x \\in B \\right \\}$

\n", "Alternatively,
\n", "$x \\in A \\cup B \\Leftrightarrow x \\in A \\; or \\; x \\in B$

\n", "The above statement says that an element is in the union if and only if the element belongs to A, B, or both.

\n", "The symbol $\\Leftrightarrow$ is a biconditional logical connective between statements and is read if and only if (iff for short)
\n", "$\\Leftrightarrow$ says that what is on the left hand side implies the right hand side and vice versa.

\n", "Example:

\n", "$\\varnothing$ is the null\\empty set.
\n", "Let A = {1,2,3}
\n", "What is $A \\cup \\varnothing$ ?

\n", "Since $\\varnothing$ has no elements, its union with A is A itself.
\n", "$A \\cup \\varnothing = A$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Venn diagram for set union" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Figure below shows the Venn diagram for union of two sets A and B. The union is the shaded area." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " $\"Union$ " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "#Testing python\n", "x = 1\n", "y = 2\n", "print(x + y)" ] } ], "metadata": { "celltoolbar": "Edit Metadata", "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.2" } }, "nbformat": 4, "nbformat_minor": 2 }

Set Union Operation.ipynb