Statements:Some paints are brushes.All brushes are varnishes.All colou...
Statements:
- Some paints are brushes.
- All brushes are varnishes.
- All colours are varnishes.
- No varnish is a canvas.
Conclusions:
I. No canvas is a brush.
II. Some paints are varnishes.
Explanation:
To determine the validity of the conclusions, we need to analyze the given statements.
From the given statements, we can infer the following:
- From the statement "Some paints are brushes," we can conclude that there is an overlap between paints and brushes.
- From the statement "All brushes are varnishes," we can infer that all brushes are a subset of varnishes.
- From the statement "All colours are varnishes," we can infer that all colors are a subset of varnishes.
- From the statement "No varnish is a canvas," we can infer that there is no overlap between varnishes and canvases.
Now let's analyze the conclusions:
I. No canvas is a brush:
- This conclusion is valid because there is no overlap between varnishes and canvases. Since brushes are a subset of varnishes, it can be concluded that no canvas is a brush.
II. Some paints are varnishes:
- This conclusion is also valid. From the given statements, we know that some paints are brushes, and all brushes are varnishes. Therefore, it can be inferred that some paints are varnishes.
Hence, both conclusions I and II follow based on the given statements.
Therefore, the correct answer is option 'E': If both conclusions I and II follow.