How can i view mathematics as a fundamental tool applicable to a wide range of discipline.

I learned a lot of things on how can identify the truth value and false. First by knowing the basic mathematical language the applicable in mathematics some of them are symbols and words. By knowing that I can learn fast in propositional calculus that i learned that the truth value is equal to 1 end the false value is 0. Propositional connecrivenes is all the simble that can use in the proposition problem. Propositions have a 6 types first is the negation of proposition that tells p is not . Then the second is conjunction proposition that tells conjunction is a compound statement formed by joining two statements with the connector and. The conjunction "P and Q" is symbolized by PQ. A conjunction is true when both of its combined parts are true; otherwise it is false. The third is disjunction inclusive "or"  that represents denoted by P v Q disjuction is a compound statement formed by joining two statements with the connector OR. The disjunction "P or Q" is symbolized by PQ. A disjunction is false if and only if both statements are false; otherwise it is true.  The fourth type is the disjunction exclusive "or" that show P or Q but not both denoted to P exclusive Q.It will be true, if exactly one of the two values is true. Otherwise it will be false. This also means that the result of 'OR' will be true only if both the values are different. Same values will result in a false. The fifth types is implication or conditional that will show if P then Q denoted by P -> Q. The sixth and lasth is biconditionals is P if and only if Q, denoted by P <-> Q. By knowing all of that proposition it helps me to identify easily the truth and false value. I can also make the truth table that needs in the problem. By making the truth table it can helps to easily show the truth value and false. Thank you for helping me to understand this type of mathematics that helps me to Identify the truth and false value.