<span>opposite or contrary in position, direction, order, or effect.
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Answer:
Consider the proposition C=(p∧q∧¬r)∨(p∧¬q∧r)∨(¬p∧q∧r)
Step-by-step explanation:
This compound proposition C uses the outer disjunction (∨) then the proposition is true if and only if one of the three propositions (p∧q∧¬r),(p∧¬q∧r),(¬p∧q∧r) is true.
First, it is impossible that two or three of these propositions are simultaneously true. For example, if (p∧q∧¬r) and (p∧¬q∧r) are both true, then ¬r is true (from the first conjuntion) and r is true (from the second one), a contradiction. All the other possibilities can be discarded reasoning in the same way.
Since these propositions are mutually excluyent, C is true if and only if exactly one of the three propositions is true (and false otherwise). This can only happen if exactly two of p,q, and r are true and the other one is false. For example, (p∧q∧¬r) is true when p and q are true, and r is false.
Answer:
Step-by-step explanation:
Chelsea is making a kite in the shape of a triangle. To determine if the triangle is a right triangle, Chelsea completed the following steps.
Step 1:
Find the side lengths of the triangle: 30 inches, 24 inches, 18 inches.
Step 2:
Substitute the values into the Pythagorean theorem: 18 squared + 24 squared = 30 squared.
Step 3:
Combine like terms: (18 + 24) squared = 30 squared.
Step 4:
Evaluate each side: 1764 not-equals 900.
Chelsea says the triangle is not a right triangle. Which best describes the accuracy of her explanation?
The triangle is actually a right triangle. In step 2, Chelsea incorrectly substituted the values into the Pythagorean theorem.
The triangle is not a right triangle, but in step 2 Chelsea incorrectly substituted the values into the Pythagorean theorem.
The triangle is actually a right triangle. In step 3, Chelsea incorrectly rewrote the expression on the left side of the equation.
The triangle is not a right triangle, but in step 3, Chelsea incorrectly rewrote the expression on the left side of the equation.
