Write the indicated statement. Use De Morgan’s Laws if necessary. If it is a cat, then it catches birds.Inverse

Determine the truth value for each simple statement. Then, using the truth values, give the truth value of the compound statement. 8 × 2 = 20 if and only if 7 + 6 = 13.

Use DeMorganʹs laws or a truth table to determine whether the two statements are equivalent. ~(p ∨ q) → r, (~p ∧ ~q)  → r

Select letters to represent the simple statements and write each statement symbolically by using parentheses then indicate whether the statement is a negation, conjunction, disjunction, conditional, or biconditional. The lights are on if and only if it is not midnight or it is wintertime.

Write the contrapositive of the statement. Then use the contrapositive to determine whether to conditional statement is true or false. If 10 does not divide the counting number, then 5 does not divide the counting number.

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its  appropriate symbol. The car is in the garage and the bicycle is in the driveway.

Determine whether the statement is a self-contradiction, an implication, a tautology (that is not also an implication), or none of these. p → (q ∨ p)

Translate the statement into symbols then construct a truth table. p = The forest is dark.q = The moon is full.The forest is dark or the moon is full.  

Determine which, if any, of the three statements are equivalent. I) If the house is not white, then the house is not small.II) The house is not white and the house is small.III) It is false that the house is white or that the house is not small.

A fertilizer ingredient commonly mined in Florida, especially east of Tampa Bay, is____.