Logic Symbols Puzzle

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Across
  1. 6. a notion for munites
  2. 7. meaning "if is true, then is also true."
  3. 8. "∵" and it is used in proofs before reasoning
  4. 9. to express the existence of a variable
  5. 11. its symbol forms letter "A" facing downwards
  6. 14. it is an operation called factorial
Down
  1. 1. a one straight line
  2. 2. a binary operation that is treated like addition
  3. 3. a caret facing downwards
  4. 4. it is also known as caret
  5. 5. “∴” a shorthand of the or relations
  6. 10. two meanings, numbers, or quantities that are the same
  7. 12. a symbol that indicates 'and'
  8. 13. (~) stands for equivalence
  9. 15. the opposite of the given mathematical statement