Question

Statements: All squares are circles.
All circles are triangles.
Some rectangles are triangles.
Conclusions: I. All circles being rectangles is a possibility.
II. Some triangles are squares.

• A. if only conclusion I follows.
• B. if only conclusion II follows.
• C. if either conclusion I or II follows.
• D. if neither conclusion I nor II follows.
• E. if both conclusions I and II follow.

Answer 1

The correct option is E if both conclusions I and II follow.

Let $Squares=S$, $Circles=C$, $Triangles=T$ and $Rectangles=R$.

Statements:

$1)S\subset C$

$2)C\subset T$

$3)T\cap R\ne \Phi$

Conclusion-I : $C\subset R$

which doesn't contradict any of the given statements.

So, Conclusion-I follows.

Conclusion-II : $T\cap S\ne \Phi$

$S\subset C\subset T\Rightarrow T\cap S\ne \Phi$

So, conclusion-II follow.

Both conclusions follow.

$\therefore$ The answer is $\left[E\right]$.