# Causal and counterfactual reasoning

[All families](README.md) · [Methods](../METHODOLOGY.md)

## VB0046

Inputs are A = 1, B = 0 and C_in = 1. Suppose the output of the upper of the two AND gates is forced to 0 whatever its inputs are. What are the circuit's outputs S and C_out?

Rules: Standard gate symbols: a D shape with a flat back is AND, a curved back with one extra curved line is XOR, a curved back is OR. A black dot marks a connection; lines that cross without a dot do not connect. Only that one AND-gate output is changed.

![Image 1, CCA0004](../images/CCA0004.png)

Image 1 credit: [en:User:Cburnett, CC BY-SA 3.0, via Wikimedia Commons (File:Full-adder.svg); credit: Own work  This W3C-unspecified vector image was created with Inkscape .](https://commons.wikimedia.org/wiki/File%3AFull-adder.svg), [CC BY-SA 3.0](https://creativecommons.org/licenses/by-sa/3.0/). See the [asset manifest](../data/assets.jsonl) for preparation notes.

Options:

- 1: S = 0, C_out = 1
- 2: S = 1, C_out = 0
- 3: S = 0, C_out = 0
- 4: The outputs are not established by the supplied circuit and rules

## VB0047

Enable E = 1 and data D = 1. Before this, the stored output Q was 0. Suppose the output of the lower AND gate is forced to 0 whatever its inputs are. What are Q and the inverted output Q-bar afterwards?

Rules: The two cross-coupled OR-with-circle gates are NOR gates. A NOR pair whose other inputs from the AND gates are both 0 keeps its previous outputs. A dot marks a connection; lines that cross without a dot do not connect.

![Image 1, CCA0050](../images/CCA0050.png)

Image 1 credit: [Oğuz Ergin, CC BY-SA 4.0, via Wikimedia Commons (File:Flip flop D mandali tr.svg); credit: Own work](https://commons.wikimedia.org/wiki/File%3AFlip_flop_D_mandali_tr.svg), [CC BY-SA 4.0](https://creativecommons.org/licenses/by-sa/4.0/). See the [asset manifest](../data/assets.jsonl) for preparation notes.

Options:

- 1: Q = 0, Q-bar = 1
- 2: Q = 1, Q-bar = 0
- 3: Q = 0, Q-bar = 0
- 4: Q = 1, Q-bar = 1

## VB0048

The depicted adder receives A = 0111 and B = 0001, with carry in 0. If the carry wire connecting the leftmost two boxes is forced to 0, what are s3 s2 s1 s0?

Rules: Each box is a one-bit full adder: sum is the total of its two input bits and incoming carry modulo 2; outgoing carry is 1 if at least two inputs are 1. Use the drawn bit labels and wiring to identify the affected stages.

![Image 1, CCA0055](../images/CCA0055.png)

Image 1 credit: [Mik81, CC0, via Wikimedia Commons (File:Ripple-carry-adder.svg); credit: Own work](https://commons.wikimedia.org/wiki/File%3ARipple-carry-adder.svg), [CC0](https://creativecommons.org/publicdomain/zero/1.0/). See the [asset manifest](../data/assets.jsonl) for preparation notes.

Options:

- 1: 1000
- 2: 0000
- 3: 0100
- 4: 0110

## VB0049

Inputs are p = 1, q = 1 and r = 0. The first gate (the leftmost, controlled by p) is removed so that it does nothing. What values appear on the 'carry' and 'parity' outputs?

Rules: Each vertical connection is a swap gate: a black dot on one line is the control, and the two crossed lines are swapped if and only if the control line carries 1. The two lowest input lines carry the constants 0 (upper) and 1 (lower). Gates act from left to right.

![Image 1, CCA0056](../images/CCA0056.png)

Image 1 credit: [Bret Mulvey, CC BY-SA 4.0, via Wikimedia Commons (File:Fredkin Full Adder.svg); credit: Own work](https://commons.wikimedia.org/wiki/File%3AFredkin_Full_Adder.svg), [CC BY-SA 4.0](https://creativecommons.org/licenses/by-sa/4.0/). See the [asset manifest](../data/assets.jsonl) for preparation notes.

Options:

- 1: carry = 0, parity = 1
- 2: carry = 1, parity = 0
- 3: carry = 0, parity = 0
- 4: carry = 1, parity = 1

## VB0186

Replace the pictured load with a150N load while keeping the same pulley routing. What free-end pull would balance it in the ideal model?

Rules: Use the ratio between the displayed balanced load and the displayed free-end pull. For an unchanged ideal routing that ratio stays constant. Ignore friction and rope weight; do not count the hanging free end as an additional load-supporting strand.

![Image 1, NC_A0070](../images/NC_A0070.png)

Image 1 credit: [Polispasto2B.jpg: Mindbuilder
derivative work: Arnaud Ramey (talk); File:Compound pulley.svg; CC BY-SA 3.0; via Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Compound_pulley.svg), [CC BY-SA 3.0](https://creativecommons.org/licenses/by-sa/3.0/). See the [asset manifest](../data/assets.jsonl) for preparation notes.

Options:

- 1: 25N
- 2: 30N
- 3: 37.5N
- 4: 75N

## VB0187

Starting from balance, double the mass on the longer arm. Which of these changes would restore balance while leaving both new masses fixed?

Rules: Use the mass-times-arm balance relation shown in the picture. In each option change only the named arm length; the other arm and the fulcrum position stay fixed. Choose among the offered actions, not every possible remedy.

![Image 1, NC_A0071](../images/NC_A0071.png)

Image 1 credit: [Tristanevanslee; File:Lever Principle 3D.svg; CC0; via Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Lever_Principle_3D.svg), [CC0](https://creativecommons.org/publicdomain/zero/1.0/). See the [asset manifest](../data/assets.jsonl) for preparation notes.

Options:

- 1: The restoring change is not established under the supplied balance rule
- 2: Halve b
- 3: Double b
- 4: Halve a

## VB0188

Close valve5 while leaving valve4 as drawn. On the next attempted downstroke of piston2, which of chambers1 and3 can receive displaced fluid through an open path from2?

Rules: For this diagram a vertical blue valve handle means closed and a diagonal handle means open. Closed valves completely block flow; open ones allow flow in either direction. Ignore leakage, fluid compression and any unpictured connections. Use the numbered chambers in the image.

![Image 1, NC_A0072](../images/NC_A0072.png)

Image 1 credit: [Wela49, Hydraulic press, CC BY-SA 3.0 via GFDL license migration, via Wikimedia Commons; canonical rasterization and metadata-free input conversion.](https://commons.wikimedia.org/wiki/File:Hydraulic_press.svg), [CC BY-SA 3.0](https://creativecommons.org/licenses/by-sa/3.0/). See the [asset manifest](../data/assets.jsonl) for preparation notes.

Options:

- 1: Neither chamber1 nor chamber3
- 2: Chamber1 only
- 3: Both chambers1 and3
- 4: Chamber3 only

## VB0189

The red shaft turns clockwise. What are the blue shaft's directions before and after replacing the pictured belt routing with a belt that crosses once?

Rules: View both shafts from the same side. In this ideal model an uncrossed belt drives both shafts in the same direction; one crossing reverses their directions. Shafts stay fixed and the belt does not slip. Read the currently drawn routing for the before case.

![Image 1, NC_A0073](../images/NC_A0073.png)

Image 1 credit: [Pradana Aumars (talk · contribs); File:Belt pulley kinematic scheme.svg; CC0; via Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Belt_pulley_kinematic_scheme.svg), [CC0](https://creativecommons.org/publicdomain/zero/1.0/). See the [asset manifest](../data/assets.jsonl) for preparation notes.

Options:

- 1: Counterclockwise before and counterclockwise after
- 2: Clockwise before and counterclockwise after
- 3: Clockwise before and clockwise after
- 4: Counterclockwise before and clockwise after

## VB0195

Disable the bottom-left transition. Starting with exactly the pictured tokens, what is the maximum number of times the bottom-right transition can fire?

Rules: Circles hold tokens and black bars are transitions. A firing consumes one token from every incoming arrow and produces one token on every outgoing arrow. Any enabled transition may fire repeatedly. Disabled transitions never fire. There are no hidden tokens or capacity limits.

![Image 1, NC_A0082](../images/NC_A0082.png)

Image 1 credit: [Msoos, Petri net example, CC BY-SA 2.5, via Wikimedia Commons; canonical rasterization and metadata-free input conversion.](https://commons.wikimedia.org/wiki/File:Petri_net_example.svg), [CC BY-SA 2.5](https://creativecommons.org/licenses/by-sa/2.5/). See the [asset manifest](../data/assets.jsonl) for preparation notes.

Options:

- 1: 3 times
- 2: 1 time
- 3: An unlimited number of times
- 4: 2 times

## VB0196

Force SPRINKLER to T externally. Under this intervention, what is the probability that GRASS WET is T?

Rules: Treat the diagram as the specified causal probability model. Forcing a node replaces its conditional probability table with the forced value and removes its incoming arrows; all other tables stay unchanged. Average over RAIN using its prior, rather than updating RAIN as if SPRINKLER had merely been observed. T and F mean true and false.

![Image 1, NC_A0083](../images/NC_A0083.png)

Image 1 credit: [AnAj; File:SimpleBayesNet.svg; Public domain; via Wikimedia Commons](https://commons.wikimedia.org/wiki/File:SimpleBayesNet.svg), [Public domain](https://commons.wikimedia.org/wiki/File:SimpleBayesNet.svg). See the [asset manifest](../data/assets.jsonl) for preparation notes.

Options:

- 1: 0.80
- 2: 0.90
- 3: 0.918
- 4: 0.99