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There are several statements in the table below.For each, determine whether it is a negation of this statement.Ivan is wearing boots.Statement Negation?Yes NoIvan is wearing sandals. Ivan is not wearing boots. Ivan is not wearing tennis shoes. It is not the case that Ivan is wearing boots.

Question

There are several statements in the table below.For each, determine whether it is a negation of this statement.Ivan is wearing boots.Statement Negation?Yes NoIvan is wearing sandals. Ivan is not wearing boots. Ivan is not wearing tennis shoes. It is not the case that Ivan is wearing boots.

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Solution

The table is asking whether each statement is a negation of the original statement "Ivan is wearing boots." Here's how to determine this:

  1. "Ivan is wearing sandals." - This is not a direct negation of the original statement. It could be possible for Ivan to wear boots and sandals at the same time (though it would be unusual). So, the answer is No.

  2. "Ivan is not wearing boots." - This is a direct negation of the original statement. It directly contradicts the statement "Ivan is wearing boots." So, the answer is Yes.

  3. "Ivan is not wearing tennis shoes." - This is not a direct negation of the original statement. The original statement is about boots, not tennis shoes. So, the answer is No.

  4. "It is not the case that Ivan is wearing boots." - This is a direct negation of the original statement. It directly contradicts the statement "Ivan is wearing boots." So, the answer is Yes.

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There are several statements in the table below.For each, determine whether it is a negation of this statement.x is not equal to 300.Statement Negation?Yes Nox is equal to 100. x is equal to 300. x is not equal to 400. It is not the case that x is equal to 400.

The second statement is a negation of the first statement.

Draw truth-table for negation.

The truth value of a negation (NOT) in a truth table is true when:a.The operand is trueb.The operand is falsec.The operand is unknownd.The operand is both true and false

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