Superposition and cancellation of overlaid figures
What this domain tests
Two or more figures are combined by a logical rule to produce a third. Your job is to identify the operation and compute the result, usually across a row of a grid or along a series.
The operations
- Union (OR): any line or region present in either input appears in the result.
- Intersection (AND): only what is common to both inputs survives.
- Cancellation (XOR): elements present in exactly one input survive; elements present in both disappear.
- Retention (A AND NOT B): elements of the first figure survive only where the second has nothing.
- Shading rules: overlapping shaded regions may invert, merge, or cancel independently of the lines.
- Layering: the later figure may simply hide what lies beneath it.
Method: build a truth table
Fix a reference layout: compass points around a circle, the seven segments of a digital display, or the cells of a small grid. For each position record presence in input 1 and input 2, then apply the candidate operation. This converts a visual puzzle into a short logical computation and makes errors visible.
Worked example
Frame 1 is a square with one diagonal. Frame 2 is the same square with a vertical midline. Frame 1 and frame 2 share the square, so under cancellation the square disappears and the result is the diagonal plus the vertical line. That is frame 3. Now combine frame 2 (square plus vertical line) with frame 3 (diagonal plus vertical line): the vertical line is common and cancels, the square and the diagonal each appear once, so frame 4 is the square with the diagonal, which is frame 1 again. The sequence has period three, and the answer options typically include a union interpretation, which keeps the square in frame 3 and breaks the cycle.
Traps that cost marks
- Treating an overlap as union when the rule is cancellation.
- Forgetting that the outer frame is an element and also cancels when common.
- Cancelling the shading while leaving the lines, or the reverse, when the rule applies to both.
- Missing that the operation may run between frames 1 and 3 to produce frame 2.
- Assuming common elements always vanish; in some items the common element is the only thing retained.