[amp_mcq option1=”None follows” option2=”Only I follows” option3=”Only I and II follow” option4=”Only II and III follow E. All follow” correct=”option1″]<\/p>\n
The correct answer is A. None follows.<\/p>\n
The first statement, “Some dogs are rats,” can be expressed in symbolic form as $D \\cap R \\neq \\emptyset$. The second statement, “All rats are trees,” can be expressed in symbolic form as $R \\subseteq T$. The third statement, “Some trees are not dogs,” can be expressed in symbolic form as $T \\setminus D \\neq \\emptyset$.<\/p>\n
We can use DeMorgan’s Law to negate the second statement: $\\neg (R \\subseteq T) \\equiv T \\setminus R \\neq \\emptyset$. This means that there are some trees that are not rats.<\/p>\n
We can also use DeMorgan’s Law to negate the third statement: $\\neg (T \\setminus D \\neq \\emptyset) \\equiv T \\cap D \\neq \\emptyset$. This means that there are some trees that are dogs.<\/p>\n
However, we cannot conclude that all trees are dogs, all dogs are trees, or all rats are dogs. This is because the first statement only tells us that some dogs are rats, and the second statement only tells us that all rats are trees. It is possible that there are dogs that are not rats, and it is also possible that there are trees that are not rats.<\/p>\n
Therefore, none of the conclusions follow.<\/p>\n","protected":false},"excerpt":{"rendered":"
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