Discrete Mathematics is the foundation of computer science, cryptography, and problem-solving in many disciplines. With Moogle Math’s Discrete Mathematics Solver, you can tackle problems related to set theory, graph theory, logic, and combinatorics, all with precision and clarity.
Set Operations
Example: Find the union and intersection of sets A = {1, 2, 3} and B = {2, 3, 4}.
Input: set_operations(A=[1, 2, 3], B=[2, 3, 4])
Logical Expressions
Example: Simplify the logical expression (A∧B)∨(¬A∧B)(A \land B) \lor (\lnot A \land B).
Input: simplify_logic(expression="(A && B) || (!A && B)")
Combinatorics
Example: Calculate the number of ways to choose 3 items from a set of 5.
Input: combinations(n=5, k=3)
Graph Theory
Example: Determine the shortest path in a graph with vertices {A, B, C, D}.
Input: shortest_path(graph={A: [B, C], B: [D], C: [D]}, start=A, end=D)
Number Theory
Example: Find the greatest common divisor (GCD) of 28 and 42.
Input: gcd(a=28, b=42)
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Example: Find the Cartesian product of sets A = {1, 2} and B = {3, 4}.
Input: cartesian_product(A=[1, 2], B=[3, 4])
Example: Solve the recurrence an=an−1+2an−2a_n = a_{n-1} + 2a_{n-2} with initial conditions a0=1,a1=1a_0 = 1, a_1 = 1.
Input: recurrence_relation(recurrence="a[n]=a[n-1]+2*a[n-2]", initial_conditions={0: 1, 1: 1})
Example: Check if a graph is bipartite for vertices {A, B, C, D}.
Input: is_bipartite(graph={A: [B, C], B: [A, D], C: [A, D], D: [B, C]})
Example: Solve for permutations of 4 items from a set of 6.
Input: permutations(n=6, k=4)